User:Tomruen/configuration

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Example 8-cube. The diagonal elements are the k-face counts. The below diagonal rows are element counts of each k-face. The above diagonal rows are the k-figure element counts.

The configuration matrix shows the number of k-face elements along the diagonal, while the nondiagonal element show the incidence counts between all elements.[1] The number of elements of its facets can be seen on the bottom row, left of the diagonal, and k-face elements above that. The top row, right of the diagonal represent the number of elements of the vertex figure. The second row contains the edge-figures, and so on. These figures are the duals of the k-faces of the dual polytope, which can be seen by rotating the matrix 180 degrees.

For regular n-polytopes, the there are only one type of element, so the matrix is n×n. For irregular polytopes, the matrix is expanded with one row per element type, which in the limit contains one row for every element. Like a general polyhedron with v vertices, e edges and f faces would have v+e+f total rows and columns.

Polygons[edit]

Regular polygons
regular polygon Triangle
Regular polygon 3.svg
Square
Regular polygon 4.svg
Pentagon
Regular polygon 5.svg
Hexagon
Regular polygon 6.svg
xno
. . | n | 2
----+---+--
x . | 2 | n
x-2n-o
.    . | 2n | 2
-------+----+---
x    . | 2  | 2n
x3o
. . | 3 | 2
----+---+--
x . | 2 | 3
x4o
. . | 4 | 2
----+---+--
x . | 2 | 4
x5o
. . | 5 | 2
----+---+--
x . | 2 | 5
x6o
. . | 6 | 2
----+---+--
x . | 2 | 6

Triangle[edit]

Triangles
Equilateral
{3}
CDel node 1.pngCDel 3.pngCDel node.png
Equilateral triangle element-labeled.png
Isosceles
{ }∨( )
CDel node 1.pngCDel join.pngCDel node.png
Isos triangle element-labeled.png
Scalene
( )∨( )∨( )
CDel node.pngCDel join.pngCDel node.pngCDel join.pngCDel node.png
Scalene triangle element-labeled.png
(v:3; e:3) (v:2+1; e:2+1) (v:1+1+1; e:1+1+1)
  | A | a 
--+---+---
A | 3 | 2 
--+---+---
a | 2 | 3 
  | A B | a b
--+-----+-----
A | 2 * | 1 1
B | * 1 | 2 0
--+-----+-----
a | 1 1 | 2 * 
b | 2 0 | * 1 
  | A B C | a b c
--+-------+-------
A | 1 * * | 0 1 1
B | * 1 * | 1 0 1 
C | * * 1 | 1 1 0 
--+-------+-------
a | 0 1 1 | 1 * * 
b | 1 0 1 | * 1 * 
c | 1 1 0 | * * 1

Quadrilateral[edit]

Quadrilaterals by symmetry
Quadrilaterals
Square
{4}
CDel node 1.pngCDel 4.pngCDel node.png
Square element-labeled.png
Rectangle
{ }×{ }
CDel node 1.pngCDel 2.pngCDel node 1.png
Rectangle element-labeled.png
Rhombus
{ }+{ }
CDel node 1.pngCDel sum.pngCDel node 1.png
Rhombus element-labeled.png
Parallelogram
Parallelogram element-labeled.png
Isosceles trapezoid
{ }||{ }
Isos trapezoid element-labeled.png
Kite
Kite element-labeled.png
General
Quadrilateral element-labeled.png
(v:4; e:4) (v:4; e:2+2) (v:2+2; e:4) (v:2+2; e:2+2) (v:2+2; e:1+1+2) (v:1+1+2; e:2+2) (v:1+1+1+1; e:1+1+1+1)
  | A | a 
--+---+---
A | 4 | 2 
--+---+---
a | 2 | 4
  | A | a b
--+---+-----
A | 4 | 1 1
--+---+-----
a | 2 | 2 * 
b | 2 | * 2 
  | A B | a
--+-----+---
A | 2 * | 2 
B | * 2 | 2 
--+-----+---
a | 1 1 | 4
  | A B | a b
--+-----+-----
A | 2 * | 1 1
B | * 2 | 1 1
--+-----+-----
a | 1 1 | 2 * 
b | 1 1 | * 2 
  | A B | a b c
--+-----+-------
A | 2 * | 1 0 1 
B | * 2 | 0 1 1
--+-----+------
a | 2 0 | 1 * *
b | 0 2 | * 1 *
c | 1 1 | * * 2 
  | A B C | a b
--+-------+----
A | 1 * * | 2 0 
B | * 1 * | 0 2
C | * * 2 | 1 1
--+-------+----
a | 1 0 1 | 2 *
b | 0 1 1 | * 2 
  | A B C D | a b c d
--+---------+--------
A | 1 * * * | 1 0 0 1
B | * 1 * * | 1 1 0 0 
C | * * 1 * | 0 1 1 0
D | * * * 1 | 0 0 1 1
--+---------+--------
a | 1 1 0 0 | 1 * * *
b | 0 1 1 0 | * 1 * *
c | 0 0 1 1 | * * 1 *
d | 1 0 0 1 | * * * 1 

Polyhedra[edit]

Regular polyhedra
Platonic solid
{p,q}
Tetrahedron [1]
{3,3}
(v:4; e:6; f:4)
Icosahedron[2]
{3,5}
(v:12; e:30; f:20)
Dodecahedron [3]
{5,3}
(v:20; e:30; f:12)
Stellated dodecahedron [4]
{5/2,5}
(v:12; e:30; f:12)
v e f
v 4p/k q q
e 2 2pq/k 2
f p p 4q/k
With k=4-(p-2)(q-2)
x3o3o
. . . | 4 | 3 | 3
------+---+---+--
x . . | 2 | 6 | 2
------+---+---+--
x3o . | 3 | 3 | 4
x3o5o
. . . | 12 |  5 |  5
------+----+----+---
x . . |  2 | 30 |  2
------+----+----+---
x3o . |  3 |  3 | 20
o3o5x
. . . | 20 |  3 |  3
------+----+----+---
. . x |  2 | 30 |  2
------+----+----+---
. o5x |  5 |  5 | 12
x5/2o5o
.   . . | 12 |  5 |  5
--------+----+----+---
x   . . |  2 | 30 |  2
--------+----+----+---
x5/2o . |  5 |  5 | 12
Octahedron [5]
{3,4}
(v:6; e:12; f:8)
Cube [6]
{4,3}
(v:8; e:12; f:6)
Great icosahedron [7]
{3,5/2}
(v:12; e:30; f:20)
Great stellated dodecahedron [8]
{5/2,3}
(v:20; e:30; f:12)
Great dodecahedron [9]
{5,5/2}
(v:12; e:30; f:12)
x3o4o
. . . | 6 |  4 | 4
------+---+----+--
x . . | 2 | 12 | 2
------+---+----+--
x3o . | 3 |  3 | 8
o3o4x
. . . | 8 |  3 | 3
------+---+----+--
. . x | 2 | 12 | 2
------+---+----+--
. o4x | 4 |  4 | 6
o5/2o3x
.   . . | 12 |  5 |  5
--------+----+----+---
.   . x |  2 | 30 |  2
--------+----+----+---
.   o3x |  3 |  3 | 20
x5/2o3o
.   . . | 20 |  3 |  3
--------+----+----+---
x   . . |  2 | 30 |  2
--------+----+----+---
x5/2o . |  5 |  5 | 12
o5/2o5x
.   . . | 12 |  5 |  5
--------+----+----+---
.   . x |  2 | 30 |  2
--------+----+----+---
.   o5x |  5 |  5 | 12

Tetrahedra[edit]

Symmetries of tetrahedra
Tetrahedra
Regular
(v:4; e:6; f:4)
Tetrahedron type1.png
tetragonal disphenoid
(v:4; e:2+4; f:4)
Tetrahedron type2.png
Rhombic disphenoid
(v:4; e:2+2+2; f:4)
Tetrahedron type3.png
Digonal disphenoid
(v:2+2; e:4+1+1; f:2+2)
Tetrahedron type6.png
Phyllic disphenoid
(v:2+2; e:2+2+1+1; f:2+2)
Tetrahedron type4.png
  A| 4 | 3 | 3
---+---+---+--
  a| 2 | 6 | 2
---+---+---+--
aaa| 3 | 3 | 4
  A| 4 | 2 1 | 3
---+---+-----+--
  a| 2 | 4 * | 2
  b| 2 | * 2 | 2
---+---+-----+--
aab| 3 | 2 1 | 4
   A| 4 | 1 1 1 | 3
----+---+-------+--
   a| 2 | 2 * * | 2
   b| 2 | * 2 * | 2
   c| 2 | * * 2 | 2
----+---+-------+--
 abc| 3 | 1 1 1 | 4
  A| 2 * | 2 1 0 | 2 1
  B| * 2 | 2 0 1 | 1 2
---+-----+-------+----
  a| 1 1 | 4 * * | 1 1
  b| 2 0 | * 1 * | 2 0
  c| 0 2 | * * 1 | 0 2
---+-----+-------+----
aab| 2 1 | 2 1 0 | 2 *
aac| 1 2 | 2 0 1 | * 2
  A| 2 * | 1 0 1 1 | 1 2
  B| * 2 | 1 1 1 0 | 2 1
---+-----+---------+----
  a| 1 1 | 2 * * * | 1 1
  b| 1 1 | * 2 * * | 1 1
  c| 0 2 | * * 1 * | 2 0
  d| 2 0 | * * * 1 | 0 2
---+-----+---------+----
abc| 1 2 | 1 1 1 0 | 2 *
bcd| 2 1 | 1 1 0 1 | * 2
Triangular pyramid
(v:3+1; e:3+3; f:3+1)
Tetrahedron type5.png
Mirrored spheroid
(v:2+1+1; e:2+2+1+1; f:2+1+1)
Tetrahedron type7.png
No symmetry
(v:1+1+1+1; e:1+1+1+1+1+1; f:1+1+1+1)
Tetrahedron type8.png
  A| 3 * | 2 1 | 2 1
  B| * 1 | 0 3 | 3 0
---+-----+-----+----
  a| 2 0 | 3 * | 1 1
  b| 1 1 | * 3 | 2 0
---+-----+-----+----
abb| 2 1 | 1 2 | 3 *
aaa| 3 0 | 3 0 | * 1
  A| 1 * * | 2 0 1 0 | 2 1 0 
  B| * 1 * | 0 2 1 0 | 2 0 1 
  C| * * 2 | 1 1 0 1 | 1 1 1 
---+-------+---------+------
  a| 1 0 1 | 2 * * * | 1 1 0 
  b| 0 1 1 | * 2 * * | 1 0 1 
  c| 1 1 0 | * * 1 * | 2 0 0 
  d| 0 0 2 | * * * 1 | 0 1 1 
---+-------+---------+------
ABC| 1 1 1 | 1 1 1 0 | 2 * *
ACC| 1 0 2 | 2 0 0 1 | * 1 *
BCC| 0 1 2 | 0 2 0 1 | * * 1
  A | 1 0 0 0 | 1 1 1 0 0 0 | 1 1 1 0
  B | 0 1 0 0 | 1 0 0 1 1 0 | 1 1 0 1
  C | 0 0 1 0 | 0 1 0 1 0 1 | 1 0 1 1
  D | 0 0 0 1 | 0 0 1 0 1 1 | 0 1 1 1
----+---------+-------------+--------
  a | 1 1 0 0 | 1 0 0 0 0 0 | 1 1 0 0
  b | 1 0 1 0 | 0 1 0 0 0 0 | 1 0 1 0
  c | 1 0 0 1 | 0 0 1 0 0 0 | 0 1 1 0
  d | 0 1 1 0 | 0 0 0 1 0 0 | 1 0 0 1
  e | 0 1 0 1 | 0 0 0 0 1 0 | 0 1 0 1
  f | 0 0 1 1 | 0 0 0 0 0 1 | 0 0 1 1
----+---------+-------------+--------
ABC | 1 1 1 0 | 1 1 0 1 0 0 | 1 0 0 0
ABD | 1 1 0 1 | 1 0 1 0 1 0 | 0 1 0 0
ACD | 1 0 1 1 | 0 1 1 0 0 1 | 0 0 1 0
BCD | 0 1 1 1 | 0 0 0 1 1 1 | 0 0 0 1

Uniform polyhedra[edit]

The vertex figure can be seen as the top row, right of diagonal.
Semiregular polyhedra in tetrahedral family
Tetratetrahedron [10] CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
(v:6; e:12; f:4+4)
Truncated tetrahedron [11] CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
(v:12; e:6+12; f:4+4)
o3x3o
. . . | 6 |  4 | 2 2
------+---+----+----
. x . | 2 | 12 | 1 1
------+---+----+----
o3x . | 3 |  3 | 4 *
. x3o | 3 |  3 | * 4
x3x3o
. . . | 12 | 1  2 | 2 1
------+----+------+----
x . . |  2 | 6  * | 2 0
. x . |  2 | * 12 | 1 1
------+----+------+----
x3x . |  6 | 3  3 | 4 *
. x3o |  3 | 0  3 | * 4
o3x3x
. . . | 12 |  2 1 | 1 2
------+----+------+----
. x . |  2 | 12 * | 1 1
. . x |  2 |  * 6 | 0 2
------+----+------+----
o3x . |  3 |  3 0 | 4 *
. x3x |  6 |  3 3 | * 4
Rhombitetratetrahedron [12] CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
(v:12; e:12+12; f:4+6+4)
Truncated tetratetrahedron [13] CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
(v:12; e:12+12; f:4+6+4)
Snub tetrahedron [14] CDel node h.pngCDel 3.pngCDel node h.pngCDel 3.pngCDel node h.png
(v:12; e:6+12+12; f:4+4+12)
x3o3x
. . . | 12 |  2  2 | 1 2 1
------+----+-------+------
x . . |  2 | 12  * | 1 1 0
. . x |  2 |  * 12 | 0 1 1
------+----+-------+------
x3o . |  3 |  3  0 | 4 * *
x . x |  4 |  2  2 | * 6 *
. o3x |  3 |  0  3 | * * 4
x3x3x
. . . | 24 |  1  1  1 | 1 1 1
------+----+----------+------
x . . |  2 | 12  *  * | 1 1 0
. x . |  2 |  * 12  * | 1 0 1
. . x |  2 |  *  * 12 | 0 1 1
------+----+----------+------
x3x . |  6 |  3  3  0 | 4 * *
x . x |  4 |  2  0  2 | * 6 *
. x3x |  6 |  0  3  3 | * * 4
s3s3s
demi( . . . ) | 12 | 1  2  2 | 1 1  3
--------------+----+---------+-------
      s 2 s   |  2 | 6  *  * | 0 0  2
sefa( s3s . ) |  2 | * 12  * | 1 0  1
sefa( . s3s ) |  2 | *  * 12 | 0 1  1
--------------+----+---------+-------
      s3s .   ♦  3 | 0  3  0 | 4 *  *
      . s3s   ♦  3 | 0  0  3 | * 4  *
sefa( s3s3s ) |  3 | 1  1  1 | * * 12
Semiregular polyhedra in octahedral family
Cuboctahedron [15] CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
(v:12; e:24; f:8+6)
Truncated cube [16] CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
(v:24; e:12+24; f:8+6)
Truncated octahedron [17] CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.png
(v:24; e:24+12; f:8+6)
o3x4o
. . . | 12 |  4 | 2 2
------+----+----+----
. x . |  2 | 24 | 1 1
------+----+----+----
o3x . |  3 |  3 | 8 *
. x4o |  4 |  4 | * 6
x3x4o
. . . | 24 |  1  2 | 2 1
------+----+-------+----
x . . |  2 | 12  * | 2 0
. x . |  2 |  * 24 | 1 1
------+----+-------+----
x3x . |  6 |  3  3 | 8 *
. x4o |  4 |  0  4 | * 6
o3x4x
. . . | 24 |  2  1 | 1 2
------+----+-------+----
. x . |  2 | 24  * | 1 1
. . x |  2 |  * 12 | 0 2
------+----+-------+----
o3x . |  3 |  3  0 | 8 *
. x4x |  8 |  4  4 | * 6
Rhombicuboctahedron [18] CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png
(v:24; e:24+24; f:8+12+6)
Truncated cuboctahedron [19] CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.png
(v:48; e:24+24+24; f:8+12+6)
Snub cube [20] CDel node h.pngCDel 3.pngCDel node h.pngCDel 4.pngCDel node h.png
(v:24; e:12+24+24; f:8+6+24)
x3o4x
. . . | 24 |  2  2 | 1  2 1
------+----+-------+-------
x . . |  2 | 24  * | 1  1 0
. . x |  2 |  * 24 | 0  1 1
------+----+-------+-------
x3o . |  3 |  3  0 | 8  * *
x . x |  4 |  2  2 | * 12 *
. o4x |  4 |  0  4 | *  * 6
x3x4x
. . . | 48 |  1  1  1 | 1  1 1
------+----+----------+-------
x . . |  2 | 24  *  * | 1  1 0
. x . |  2 |  * 24  * | 1  0 1
. . x |  2 |  *  * 24 | 0  1 1
------+----+----------+-------
x3x . |  6 |  3  3  0 | 8  * *
x . x |  4 |  2  0  2 | * 12 *
. x4x |  8 |  0  4  4 | *  * 6
s3s4s
demi( . . . ) | 24 |  1  2  2 | 1 1  3
--------------+----+----------+-------
      s 2 s   ♦  2 | 12  *  * | 0 0  2
sefa( s3s . ) |  2 |  * 24  * | 1 0  1
sefa( . s4s ) |  2 |  *  * 24 | 0 1  1
--------------+----+----------+-------
      s3s .   ♦  3 |  0  3  0 | 8 *  *
      . s4s   ♦  4 |  0  0  4 | * 6  *
sefa( s3s4s ) |  3 |  1  1  1 | * * 24
Semiregular polyhedra in icosahedron family
Icosidodecahedron [21] CDel node.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel node.png
(v:30; e:60; f:20+12)
Truncated dodecahedron [22] CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel node.png
(v:60; e:30+60; f:20+12)
Truncated icosahedron [23] CDel node.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel node 1.png
(v:60; e:60+30; f:20+12)
o3x5o
. . . | 30 |  4 |  2  2
------+----+----+------
. x . |  2 | 60 |  1  1
------+----+----+------
o3x . |  3 |  3 | 20  *
. x5o |  5 |  5 |  * 12
x3x5o
. . . | 60 |  1  2 |  2  1
------+----+-------+------
x . . |  2 | 30  * |  2  0
. x . |  2 |  * 60 |  1  1
------+----+-------+------
x3x . |  6 |  3  3 | 20  *
. x5o |  5 |  0  5 |  * 12
o3x5x
. . . | 60 |  2  1 |  1  2
------+----+-------+------
. x . |  2 | 60  * |  1  1
. . x |  2 |  * 30 |  0  2
------+----+-------+------
o3x . |  3 |  3  0 | 20  *
. x5x | 10 |  5  5 |  * 12
Rhombicosidodecahedron [24] CDel node 1.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node 1.png
(v:60; e:60+60; f:20+30+12)
Truncated icosidodecahedron [25] CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel node 1.png
(v:120; e:60+60+60; f:20+30+12)
Snub dodecahedron [26] CDel node h.pngCDel 3.pngCDel node h.pngCDel 5.pngCDel node h.png
(v:60; e:30+60+60; f:20+12+60)
x3o5x
. . . | 60 |  2  2 |  1  2  1
------+----+-------+---------
x . . |  2 | 60  * |  1  1  0
. . x |  2 |  * 60 |  0  1  1
------+----+-------+---------
x3o . |  3 |  3  0 | 20  *  *
x . x |  4 |  2  2 |  * 30  *
. o5x |  5 |  0  5 |  *  * 12
x3x5x
. . . | 120 |  1  1  1 |  1  1  1
------+-----+----------+---------
x . . |   2 | 60  *  * |  1  1  0
. x . |   2 |  * 60  * |  1  0  1
. . x |   2 |  *  * 60 |  0  1  1
------+-----+----------+---------
x3x . |   6 |  3  3  0 | 20  *  *
x . x |   4 |  2  0  2 |  * 30  *
. x5x |  10 |  0  5  5 |  *  * 12
s3s5s
demi( . . . ) | 60 |  1  2  2 |  1  1  3
--------------+----+----------+---------
      s 2 s   ♦  2 | 30  *  * |  0  0  2
sefa( s3s . ) |  2 |  * 60  * |  1  0  1
sefa( . s5s ) |  2 |  *  * 60 |  0  1  1
--------------+----+----------+---------
      s3s .   ♦  3 |  0  3  0 | 20  *  *
      . s5s   ♦  5 |  0  0  5 |  * 12  *
sefa( s3s5s ) |  3 |  1  1  1 |  *  * 60

Higher polytopes[edit]

4D[edit]

Regular 4-polytopes[edit]

4D
{p,q,r} 5-cell {3,3,3} [27] 16-cell {3,3,4} [28] 600-cell {3,3,5} [29] 120-cell {5,3,3} [30]
v e f c
v f0 4q/k2 2qr\k2 4r\k2
e 2 f1 r r
f p p f2 2
c 4p/k1 2pq/k1 4q/k1 f3
With k1=4-(p-2)(q-2)
With k2=4-(q-2)(r-2)
f0=order([p,q,r])/order([q,r])
f1=order([p,q,r])/order([])/order([r])
f2=order([p,q,r])/order([])/order([p])
f3=order([p,q,r])/order([p,q])
x3o3o3o
. . . . | 5 ♦  4 |  6 | 4
--------+---+----+----+--
x . . . | 2 | 10 |  3 | 3
--------+---+----+----+--
x3o . . | 3 |  3 | 10 | 2
--------+---+----+----+--
x3o3o . ♦ 4 |  6 |  4 | 5
x3o3o4o
. . . . | 8 ♦  6 | 12 |  8
--------+---+----+----+---
x . . . | 2 | 24 |  4 |  4
--------+---+----+----+---
x3o . . | 3 |  3 | 32 |  2
--------+---+----+----+---
x3o3o . ♦ 4 |  6 |  4 | 16
x3o3o5o
. . . . | 120 ♦  12 |   30 |  20
--------+-----+-----+------+----
x . . . |   2 | 720 |    5 |   5
--------+-----+-----+------+----
x3o . . |   3 |   3 | 1200 |   2
--------+-----+-----+------+----
x3o3o . ♦   4 |   6 |    4 | 600
o3o3o5x
. . . . | 600 ♦    4 |   6 |   4
--------+-----+------+-----+----
. . . x |   2 | 1200 |   3 |   3
--------+-----+------+-----+----
. . o5x |   5 |    5 | 720 |   2
--------+-----+------+-----+----
. o3o5x ♦  20 |   30 |  12 | 120
24-cell {3,4,3} [31] tesseract {4,3,3} [32] grand 600-cell {3,3,5/2} [33] great grand stellated 120-cell {5/2,3,3} [34]
x3o4o3o
. . . . | 24 ♦  8 | 12 |  6
--------+----+----+----+---
x . . . |  2 | 96 |  3 |  3
--------+----+----+----+---
x3o . . |  3 |  3 | 96 |  2
--------+----+----+----+---
x3o4o . ♦  6 | 12 |  8 | 24
o3o3o4x
. . . . | 16 ♦  4 |  6 | 4
--------+----+----+----+--
. . . x |  2 | 32 |  3 | 3
--------+----+----+----+--
. . o4x |  4 |  4 | 24 | 2
--------+----+----+----+--
. o3o4x ♦  8 | 12 |  6 | 8
x3o3o5/2o
. . .   . | 120 ♦  12 |   30 |  20
----------+-----+-----+------+----
x . .   . |   2 | 720 |    5 |   5
----------+-----+-----+------+----
x3o .   . |   3 |   3 | 1200 |   2
----------+-----+-----+------+----
x3o3o   . ♦   4 |   6 |    4 | 600
o3o3o5/2x
. . .   . | 600 ♦    4 |   6 |   4
----------+-----+------+-----+----
. . .   x |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
. . o5/2x |   5 |    5 | 720 |   2
----------+-----+------+-----+----
. o3o5/2x ♦  20 |   30 |  12 | 120
great stellated 120-cell {5/2,3,5} [35] icosahedral 120-cell {3,5,5/2} [36] small stellated 120-cell {5/2,5,3} [37] great 120-cell {5,5/2,5} [38]
o5o3o5/2x
. . .   . | 120 ♦  12 |  30 |  20
----------+-----+-----+-----+----
. . .   x |   2 | 720 |   5 |   5
----------+-----+-----+-----+----
. . o5/2x |   5 |   5 | 720 |   2
----------+-----+-----+-----+----
. o3o5/2x ♦  20 |  30 |  12 | 120
x3o5o5/2o
. . .   . | 120 ♦  12 |   30 |  12
----------+-----+-----+------+----
x . .   . |   2 | 720 |    5 |   5
----------+-----+-----+------+----
x3o .   . |   3 |   3 | 1200 |   2
----------+-----+-----+------+----
x3o5o   . ♦  12 |  30 |   20 | 120
x5/2o5o3o
.   . . . | 120 ♦   20 |  30 |  12
----------+-----+------+-----+----
x   . . . |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
x5/2o . . |   5 |    5 | 720 |   2
----------+-----+------+-----+----
x5/2o5o . ♦  12 |   30 |  12 | 120
x5o5/2o5o
. .   . . | 120 ♦  12 |  30 |  12
----------+-----+-----+-----+----
x .   . . |   2 | 720 |   5 |   5
----------+-----+-----+-----+----
x5o   . . |   5 |   5 | 720 |   2
----------+-----+-----+-----+----
x5o5/2o . ♦  12 |  30 |  12 | 120
grand 120-cell {5,3,5/2} [39] great icosahedral 120-cell {3,5/2,5} [40] great grand 120-cell {5,5/2,3} [41] grand stellated 120-cell {5/2,5,5/2} [42]
x5o3o5/2o
. . .   . | 120 ♦  12 |  30 |  20
----------+-----+-----+-----+----
x . .   . |   2 | 720 |   5 |   5
----------+-----+-----+-----+----
x5o .   . |   5 |   5 | 720 |   2
----------+-----+-----+-----+----
x5o3o   . ♦  20 |  30 |  12 | 120
x3o5/2o5o
. .   . . | 120 ♦  12 |   30 |  12
----------+-----+-----+------+----
x .   . . |   2 | 720 |    5 |   5
----------+-----+-----+------+----
x3o   . . |   3 |   3 | 1200 |   2
----------+-----+-----+------+----
x3o5/2o . ♦  12 |  30 |   20 | 120
x5o5/2o3o
. .   . . | 120 ♦   20 |  30 |  12
----------+-----+------+-----+----
x .   . . |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
x5o   . . |   5 |    5 | 720 |   2
----------+-----+------+-----+----
x5o5/2o . ♦  12 |   30 |  12 | 120
x5/2o5o5/2o
.   . . . | 120 ♦  12 |  30 |  12
----------+-----+-----+-----+----
x   . . . |   2 | 720 |   5 |   5
----------+-----+-----+-----+----
x5/2o . . |   5 |   5 | 720 |   2
----------+-----+-----+-----+----
x5/2o5o . ♦  12 |  30 |  12 | 120

5-cells[edit]

5-cells
5-cell {3,3,3} [43] Tetrahedral pyramid {3,3}∨( ) {3}∨{ }
x3o3o3o
. . . . | 5 ♦  4 |  6 | 4
--------+---+----+----+--
x . . . | 2 | 10 |  3 | 3
--------+---+----+----+--
x3o . . | 3 |  3 | 10 | 2
--------+---+----+----+--
x3o3o . ♦ 4 |  6 |  4 | 5
(pt || tet)

o.3o.3o.    | 1 * ♦ 4 0 | 6 0 | 4 0
.o3.o3.o    | * 4 ♦ 1 3 | 3 3 | 3 1
------------+-----+-----+-----+----
oo3oo3oo&#x | 1 1 | 4 * | 3 0 | 3 0
.x .. ..    | 0 2 | * 6 | 1 2 | 2 1
------------+-----+-----+-----+----
ox .. ..&#x | 1 2 | 2 1 | 6 * | 2 0
.x3.o ..    | 0 3 | 0 3 | * 4 | 1 1
------------+-----+-----+-----+----
ox3oo ..&#x ♦ 1 3 | 3 3 | 3 1 | 4 *
.x3.o3.o    ♦ 0 4 | 0 6 | 0 4 | * 1
(line || perp {3})
o. o.3o.    | 2 * ♦ 1 3 0 | 3 3 0 | 3 1
.o .o3.o    | * 3 ♦ 0 2 2 | 1 4 1 | 2 2
------------+-----+-------+-------+----
x. .. ..    | 2 0 | 1 * * | 3 0 0 | 3 0
oo oo3oo&#x | 1 1 | * 6 * | 1 2 0 | 2 1
.. .x ..    | 0 2 | * * 3 | 0 2 1 | 1 2
------------+-----+-------+-------+----
xo .. ..&#x | 2 1 | 1 2 0 | 3 * * | 2 0
.. ox ..&#x | 1 2 | 0 2 1 | * 6 * | 1 1
.. .x3.o    | 0 3 | 0 0 3 | * * 1 | 0 2
------------+-----+-------+-------+----
xo ox ..&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 3 *
.. ox3oo&#x ♦ 1 3 | 0 3 3 | 0 3 1 | * 2
{3}∨( )∨( ) Digonal disphenoid pyramid, { }∨{ }∨( )
( (pt || {3}) || pt)

o..3o..    | 1 * * ♦ 3 1 0 0 | 3 3 0 0 | 1 3 0
.o.3.o.    | * 3 * ♦ 1 0 2 1 | 2 1 1 2 | 1 2 1
..o3..o    | * * 1 ♦ 0 1 0 3 | 0 3 0 3 | 0 3 1
-----------+-------+---------+---------+------
oo.3oo.&#x | 1 1 0 | 3 * * * | 2 1 0 0 | 1 2 0
o.o3o.o&#x | 1 0 1 | * 1 * * | 0 3 0 0 | 0 3 0
.x. ...    | 0 2 0 | * * 3 * | 1 0 1 1 | 1 1 1
.oo3.oo&#x | 0 1 1 | * * * 3 | 0 1 0 2 | 0 2 1
-----------+-------+---------+---------+------
ox. ...&#x | 1 2 0 | 2 0 1 0 | 3 * * * | 1 1 0
ooo ...&#x | 1 1 1 | 1 1 0 1 | * 3 * * | 0 2 0
.x.3.o.    | 0 3 0 | 0 0 3 0 | * * 1 * | 1 0 1
.xo ...&#x | 0 2 1 | 0 0 1 2 | * * * 3 | 0 1 1
-----------+-------+---------+---------+------
ox.3oo.&#x ♦ 1 3 0 | 3 0 3 0 | 3 0 1 0 | 1 * *
oxo ...&#x ♦ 1 2 1 | 2 1 1 2 | 1 2 0 1 | * 3 *
.xo3.oo&#x ♦ 0 3 1 | 0 0 3 3 | 0 0 1 3 | * * 1
( (pt || line) || perp line)

o.. o..    | 1 * * ♦ 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0
.o. .o.    | * 2 * ♦ 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
..o ..o    | * * 2 ♦ 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
-----------+-------+-----------+-----------+------
oo. oo.&#x | 1 1 0 | 2 * * * * | 1 2 0 0 0 | 2 1 0
o.o o.o&#x | 1 0 1 | * 2 * * * | 0 2 1 0 0 | 1 2 0
.x. ...    | 0 2 0 | * * 1 * * | 1 0 0 2 0 | 2 0 1
.oo .oo&#x | 0 1 1 | * * * 4 * | 0 1 0 1 1 | 1 1 1
... ..x    | 0 0 2 | * * * * 1 | 0 0 1 0 2 | 0 2 1
-----------+-------+-----------+-----------+------
ox. ...&#x | 1 2 0 | 2 0 1 0 0 | 1 * * * * | 2 0 0
ooo ooo&#x | 1 1 1 | 1 1 0 1 0 | * 4 * * * | 1 1 0
... o.x&#x | 1 0 2 | 0 2 0 0 1 | * * 1 * * | 0 2 0
.xo ...&#x | 0 2 1 | 0 0 1 2 0 | * * * 2 * | 1 0 1
... .ox&#x | 0 1 2 | 0 0 0 2 1 | * * * * 2 | 0 1 1
-----------+-------+-----------+-----------+------
oxo ...&#x ♦ 1 2 1 | 2 1 1 2 0 | 1 2 0 1 0 | 2 * *
... oox&#x ♦ 1 1 2 | 1 2 0 2 1 | 0 2 1 0 1 | * 2 *
.xo .ox&#x ♦ 0 2 2 | 0 0 1 4 1 | 0 0 0 2 2 | * * 1

Uniform 4D[edit]

A4 family
o3x3o3o - rap
. . . . | 10 ♦  6 |  3  6 | 3 2
--------+----+----+-------+----
. x . . |  2 | 30 |  1  2 | 2 1
--------+----+----+-------+----
o3x . . |  3 |  3 | 10  * | 2 0
. x3o . |  3 |  3 |  * 20 | 1 1
--------+----+----+-------+----
o3x3o . ♦  6 | 12 |  4  4 | 5 *
. x3o3o ♦  4 |  6 |  0  4 | * 5
x3x3o3o - tip
. . . . | 20 |  1  3 |  3  3 | 3 1
--------+----+-------+-------+----
x . . . |  2 | 10  * |  3  0 | 3 0
. x . . |  2 |  * 30 |  1  2 | 2 1
--------+----+-------+-------+----
x3x . . |  6 |  3  3 | 10  * | 2 0
. x3o . |  3 |  0  3 |  * 20 | 1 1
--------+----+-------+-------+----
x3x3o . ♦ 12 |  6 12 |  4  4 | 5 *
. x3o3o ♦  4 |  0  6 |  0  4 | * 5
x3o3x3o - srip
. . . . | 30 ♦  2  4 |  1  4  2  2 | 2  2 1
--------+----+-------+-------------+-------
x . . . |  2 | 30  * |  1  2  0  0 | 2  1 0
. . x . |  2 |  * 60 |  0  1  1  1 | 1  1 1
--------+----+-------+-------------+-------
x3o . . |  3 |  3  0 | 10  *  *  * | 2  0 0
x . x . |  4 |  2  2 |  * 30  *  * | 1  1 0
. o3x . |  3 |  0  3 |  *  * 20  * | 1  0 1
. . x3o |  3 |  0  3 |  *  *  * 20 | 0  1 1
--------+----+-------+-------------+-------
x3o3x . ♦ 12 | 12 12 |  4  6  4  0 | 5  * *
x . x3o ♦  6 |  3  6 |  0  3  0  2 | * 10 *
. o3x3o ♦  6 |  0 12 |  0  0  4  4 | *  * 5
x3o3o3x - spid
. . . . | 20 ♦  3  3 |  3  6  3 | 1  3  3 1
--------+----+-------+----------+----------
x . . . |  2 | 30  * |  2  2  0 | 1  2  1 0
. . . x |  2 |  * 30 |  0  2  2 | 0  1  2 1
--------+----+-------+----------+----------
x3o . . |  3 |  3  0 | 20  *  * | 1  1  0 0
x . . x |  4 |  2  2 |  * 30  * | 0  1  1 0
. . o3x |  3 |  0  3 |  *  * 20 | 0  0  1 1
--------+----+-------+----------+----------
x3o3o . ♦  4 |  6  0 |  4  0  0 | 5  *  * *
x3o . x ♦  6 |  6  3 |  2  3  0 | * 10  * *
x . o3x ♦  6 |  3  6 |  0  3  2 | *  * 10 *
. o3o3x ♦  4 |  0  6 |  0  0  4 | *  *  * 5
o3x3x3o - deca
. . . . | 30 |  2  2 |  1  4  1 | 2 2
--------+----+-------+----------+----
. x . . |  2 | 30  * |  1  2  0 | 2 1
. . x . |  2 |  * 30 |  0  2  1 | 1 2
--------+----+-------+----------+----
o3x . . |  3 |  3  0 | 10  *  * | 2 0
. x3x . |  6 |  3  3 |  * 20  * | 1 1
. . x3o |  3 |  0  3 |  *  * 10 | 0 2
--------+----+-------+----------+----
o3x3x . ♦ 12 | 12  6 |  4  4  0 | 5 *
. x3x3o ♦ 12 |  6 12 |  0  4  4 | * 5
x3x3x3o - grip
. . . . | 60 |  1  1  2 |  1  2  2  1 | 2  1 1
--------+----+----------+-------------+-------
x . . . |  2 | 30  *  * |  1  2  0  0 | 2  1 0
. x . . |  2 |  * 30  * |  1  0  2  0 | 2  0 1
. . x . |  2 |  *  * 60 |  0  1  1  1 | 1  1 1
--------+----+----------+-------------+-------
x3x . . |  6 |  3  3  0 | 10  *  *  * | 2  0 0
x . x . |  4 |  2  0  2 |  * 30  *  * | 1  1 0
. x3x . |  6 |  0  3  3 |  *  * 20  * | 1  0 1
. . x3o |  3 |  0  0  3 |  *  *  * 20 | 0  1 1
--------+----+----------+-------------+-------
x3x3x . ♦ 24 | 12 12 12 |  4  6  4  0 | 5  * *
x . x3o ♦  6 |  3  0  6 |  0  3  0  2 | * 10 *
. x3x3o ♦ 12 |  0  6 12 |  0  0  4  4 | *  * 5
x3x3o3x - prip
. . . . | 60 |  1  2  2 |  2  2  1  2  1 | 1  2  1 1
--------+----+----------+----------------+----------
x . . . |  2 | 30  *  * |  2  2  0  0  0 | 1  2  1 0
. x . . |  2 |  * 60  * |  1  0  1  1  0 | 1  1  0 1
. . . x |  2 |  *  * 60 |  0  1  0  1  1 | 0  1  1 1
--------+----+----------+----------------+----------
x3x . . |  6 |  3  3  0 | 20  *  *  *  * | 1  1  0 0
x . . x |  4 |  2  0  2 |  * 30  *  *  * | 0  1  1 0
. x3o . |  3 |  0  3  0 |  *  * 20  *  * | 1  0  0 1
. x . x |  4 |  0  2  2 |  *  *  * 30  * | 0  1  0 1
. . o3x |  3 |  0  0  3 |  *  *  *  * 20 | 0  0  1 1
--------+----+----------+----------------+----------
x3x3o . ♦ 12 |  6 12  0 |  4  0  4  0  0 | 5  *  * *
x3x . x ♦ 12 |  6  6  6 |  2  3  0  3  0 | * 10  * *
x . o3x ♦  6 |  3  0  6 |  0  3  0  0  2 | *  * 10 *
. x3o3x ♦ 12 |  0 12 12 |  0  0  4  6  4 | *  *  * 5
x3x3x3x - gippid
. . . . | 120 |  1  1  1  1 |  1  1  1  1  1  1 | 1  1  1 1
--------+-----+-------------+-------------------+----------
x . . . |   2 | 60  *  *  * |  1  1  1  0  0  0 | 1  1  1 0
. x . . |   2 |  * 60  *  * |  1  0  0  1  1  0 | 1  1  0 1
. . x . |   2 |  *  * 60  * |  0  1  0  1  0  1 | 1  0  1 1
. . . x |   2 |  *  *  * 60 |  0  0  1  0  1  1 | 0  1  1 1
--------+-----+-------------+-------------------+----------
x3x . . |   6 |  3  3  0  0 | 20  *  *  *  *  * | 1  1  0 0
x . x . |   4 |  2  0  2  0 |  * 30  *  *  *  * | 1  0  1 0
x . . x |   4 |  2  0  0  2 |  *  * 30  *  *  * | 0  1  1 0
. x3x . |   6 |  0  3  3  0 |  *  *  * 20  *  * | 1  0  0 1
. x . x |   4 |  0  2  0  2 |  *  *  *  * 30  * | 0  1  0 1
. . x3x |   6 |  0  0  3  3 |  *  *  *  *  * 20 | 0  0  1 1
--------+-----+-------------+-------------------+----------
x3x3x . ♦  24 | 12 12 12  0 |  4  6  0  4  0  0 | 5  *  * *
x3x . x ♦  12 |  6  6  0  6 |  2  0  3  0  3  0 | * 10  * *
x . x3x ♦  12 |  6  0  6  6 |  0  3  3  0  0  2 | *  * 10 *
. x3x3x ♦  24 |  0 12 12 12 |  0  0  0  4  6  4 | *  *  * 5
D4 family
4-demicube {3,31,1} [44] 24-cell {31,1,1} [45]
x3o3o *b3o - hex
. . .    . | 8 ♦  6 | 12 | 4 4
-----------+---+----+----+----
x . .    . | 2 | 24 |  4 | 2 2
-----------+---+----+----+----
x3o .    . | 3 |  3 | 32 | 1 1
-----------+---+----+----+----
x3o3o    . ♦ 4 |  6 |  4 | 8 *
x3o . *b3o ♦ 4 |  6 |  4 | * 8
o3x3o *b3o - ico
. . .    . | 24 ♦  8 |  4  4  4 | 2 2 2
-----------+----+----+----------+------
. x .    . |  2 | 96 |  1  1  1 | 1 1 1
-----------+----+----+----------+------
o3x .    . |  3 |  3 | 32  *  * | 1 1 0
. x3o    . |  3 |  3 |  * 32  * | 1 0 1
. x . *b3o |  3 |  3 |  *  * 32 | 0 1 1
-----------+----+----+----------+------
o3x3o    . ♦  6 | 12 |  4  4  0 | 8 * *
o3x . *b3o ♦  6 | 12 |  4  0  4 | * 8 *
. x3o *b3o ♦  6 | 12 |  0  4  4 | * * 8
B4 family
o3x3o4o - ico
. . . . | 24 ♦  8 |  4  8 |  4 2
--------+----+----+-------+-----
. x . . |  2 | 96 |  1  2 |  2 1
--------+----+----+-------+-----
o3x . . |  3 |  3 | 32  * |  2 0
. x3o . |  3 |  3 |  * 64 |  1 1
--------+----+----+-------+-----
o3x3o . ♦  6 | 12 |  4  4 | 16 *
. x3o4o ♦  6 | 12 |  0  8 |  * 8
|
o3o3x4o - rit
. . . . | 32 ♦  6 |  6  3 |  2 3
--------+----+----+-------+-----
. . x . |  2 | 96 |  1  2 |  1 2
--------+----+----+-------+-----
. o3x . |  3 |  3 | 64  * |  1 1
. . x4o |  4 |  4 |  * 24 |  0 2
--------+----+----+-------+-----
o3o3x . ♦  4 |  6 |  4  0 | 16 *
. o3x4o ♦ 12 | 24 |  8  6 |  * 8
x3x3o4o - thex
. . . . | 48 |  1  4 |  4  4 |  4 1
--------+----+-------+-------+-----
x . . . |  2 | 24  * |  4  0 |  4 0
. x . . |  2 |  * 96 |  1  2 |  2 1
--------+----+-------+-------+-----
x3x . . |  6 |  3  3 | 32  * |  2 0
. x3o . |  3 |  0  3 |  * 64 |  1 1
--------+----+-------+-------+-----
x3x3o . ♦ 12 |  6 12 |  4  4 | 16 *
. x3o4o ♦  6 |  0 12 |  0  8 |  * 8
x3o3x4o - rico
. . . . | 96 ♦  2   4 |  1  4  2  2 |  2  2 1
--------+----+--------+-------------+--------
x . . . |  2 | 96   * |  1  2  0  0 |  2  1 0
. . x . |  2 |  * 192 |  0  1  1  1 |  1  1 1
--------+----+--------+-------------+--------
x3o . . |  3 |  3   0 | 32  *  *  * |  2  0 0
x . x . |  4 |  2   2 |  * 96  *  * |  1  1 0
. o3x . |  3 |  0   3 |  *  * 64  * |  1  0 1
. . x4o |  4 |  0   4 |  *  *  * 48 |  0  1 1
--------+----+--------+-------------+--------
x3o3x . ♦ 12 | 12  12 |  4  6  4  0 | 16  * *
x . x4o ♦  8 |  4   8 |  0  4  0  2 |  * 24 *
. o3x4o ♦ 12 |  0  24 |  0  0  8  6 |  *  * 8
x3o3o4x - sidpith
. . . . | 64 |  3  3 |  3  6  3 |  1  3  3 1
--------+----+-------+----------+-----------
x . . . |  2 | 96  * |  2  2  0 |  1  2  1 0
. . . x |  2 |  * 96 |  0  2  2 |  0  1  2 1
--------+----+-------+----------+-----------
x3o . . |  3 |  3  0 | 64  *  * |  1  1  0 0
x . . x |  4 |  2  2 |  * 96  * |  0  1  1 0
. . o4x |  4 |  0  4 |  *  * 48 |  0  0  1 1
--------+----+-------+----------+-----------
x3o3o . ♦  4 |  6  0 |  4  0  0 | 16  *  * *
x3o . x ♦  6 |  6  3 |  2  3  0 |  * 32  * *
x . o4x ♦  8 |  4  8 |  0  4  2 |  *  * 24 *
. o3o4x ♦  8 |  0 12 |  0  0  6 |  *  *  * 8
o3x3x4o - tah
. . . . | 96 |  2  2 |  1  4  1 |  2 2
--------+----+-------+----------+-----
. x . . |  2 | 96  * |  1  2  0 |  2 1
. . x . |  2 |  * 96 |  0  2  1 |  1 2
--------+----+-------+----------+-----
o3x . . |  3 |  3  0 | 32  *  * |  2 0
. x3x . |  6 |  3  3 |  * 64  * |  1 1
. . x4o |  4 |  0  4 |  *  * 24 |  0 2
--------+----+-------+----------+-----
o3x3x . ♦ 12 | 12  6 |  4  4  0 | 16 *
. x3x4o ♦ 24 | 12 24 |  0  8  6 |  * 8
o3x3o4x - srit
. . . . | 96 |   4  2 |  2  2  4  1 |  1  2 2  (A),(B)
--------+----+--------+-------------+--------
. x . . |  2 | 192  * |  1  1  1  0 |  1  1 1  (1),(/),(\)
. . . x |  2 |   * 96 |  0  0  2  1 |  0  1 2  (2),(3)
--------+----+--------+-------------+--------
o3x . . |  3 |   3  0 | 64  *  *  * |  1  1 0
. x3o . |  3 |   3  0 |  * 64  *  * |  1  0 1
. x . x |  4 |   2  2 |  *  * 96  * |  0  1 1
. . o4x |  4 |   0  4 |  *  *  * 24 |  0  0 2
--------+----+--------+-------------+--------
o3x3o . ♦  6 |  12  0 |  4  4  0  0 | 16  * *
o3x . x ♦  6 |   6  3 |  2  0  3  0 |  * 32 *
. x3o4x ♦ 24 |  24 24 |  0  8 12  6 |  *  * 8
o3o3x4x - tat
. . . . | 64 |  3  1 |  3  3 |  1 3
--------+----+-------+-------+-----
. . x . |  2 | 96  * |  2  1 |  1 2
. . . x |  2 |  * 32 |  0  3 |  0 3
--------+----+-------+-------+-----
. o3x . |  3 |  3  0 | 64  * |  1 1
. . x4x |  8 |  4  4 |  * 24 |  0 2
--------+----+-------+-------+-----
o3o3x . ♦  4 |  6  0 |  4  0 | 16 *
. o3x4x ♦ 24 | 24 12 |  8  6 |  * 8
x3x3x4o - tico
. . . . | 192 |  1  1   2 |  1  2  2  1 |  2  1 1
--------+-----+-----------+-------------+--------
x . . . |   2 | 96  *   * |  1  2  0  0 |  2  1 0
. x . . |   2 |  * 96   * |  1  0  2  0 |  2  0 1
. . x . |   2 |  *  * 192 |  0  1  1  1 |  1  1 1
--------+-----+-----------+-------------+--------
x3x . . |   6 |  3  3   0 | 32  *  *  * |  2  0 0
x . x . |   4 |  2  0   2 |  * 96  *  * |  1  1 0
. x3x . |   6 |  0  3   3 |  *  * 64  * |  1  0 1
. . x4o |   4 |  0  0   4 |  *  *  * 48 |  0  1 1
--------+-----+-----------+-------------+--------
x3x3x . ♦  24 | 12 12  12 |  4  6  4  0 | 16  * *
x . x4o ♦   8 |  4  0   8 |  0  4  0  2 |  * 24 *
. x3x4o ♦  24 |  0 12  24 |  0  0  8  6 |  *  * 8
x3x3o4x - prit
. . . . | 192 |  1   2   2 |  2  2  1  2  1 |  1  2  1 1
--------+-----+------------+----------------+-----------
x . . . |   2 | 96   *   * |  2  2  0  0  0 |  1  2  1 0
. x . . |   2 |  * 192   * |  1  0  1  1  0 |  1  1  0 1
. . . x |   2 |  *   * 192 |  0  1  0  1  1 |  0  1  1 1
--------+-----+------------+----------------+-----------
x3x . . |   6 |  3   3   0 | 64  *  *  *  * |  1  1  0 0
x . . x |   4 |  2   0   2 |  * 96  *  *  * |  0  1  1 0
. x3o . |   3 |  0   3   0 |  *  * 64  *  * |  1  0  0 1
. x . x |   4 |  0   2   2 |  *  *  * 96  * |  0  1  0 1
. . o4x |   4 |  0   0   4 |  *  *  *  * 48 |  0  0  1 1
--------+-----+------------+----------------+-----------
x3x3o . ♦  12 |  6  12   0 |  4  0  4  0  0 | 16  *  * *
x3x . x ♦  12 |  6   6   6 |  2  3  0  3  0 |  * 32  * *
x . o4x ♦   8 |  4   0   8 |  0  4  0  0  2 |  *  * 24 *
. x3o4x ♦  24 |  0  24  24 |  0  0  8 12  6 |  *  *  * 8
x3o3x4x - proh
. . . . | 192 |   2   2  1 |  1  2  2  1  2 |  1  1  2 1
--------+-----+------------+----------------+-----------
x . . . |   2 | 192   *  * |  1  1  1  0  0 |  1  1  1 0
. . x . |   2 |   * 192  * |  0  1  0  1  1 |  1  0  1 1
. . . x |   2 |   *   * 96 |  0  0  2  0  2 |  0  1  2 1
--------+-----+------------+----------------+-----------
x3o . . |   3 |   3   0  0 | 64  *  *  *  * |  1  1  0 0
x . x . |   4 |   2   2  0 |  * 96  *  *  * |  1  0  1 0
x . . x |   4 |   2   0  2 |  *  * 96  *  * |  0  1  1 0
. o3x . |   3 |   0   3  0 |  *  *  * 64  * |  1  0  0 1
. . x4x |   8 |   0   4  4 |  *  *  *  * 48 |  0  0  1 1
--------+-----+------------+----------------+-----------
x3o3x . ♦  12 |  12  12  0 |  4  6  0  4  0 | 16  *  * *
x3o . x ♦   6 |   6   0  3 |  2  0  3  0  0 |  * 32  * *
x . x4x ♦  16 |   8   8  8 |  0  4  4  0  2 |  *  * 24 *
. o3x4x ♦  24 |   0  24 12 |  0  0  0  8  6 |  *  *  * 8
o3x3x4x - grit
. . . . | 192 |   2  1  1 |  1  2  2  1 |  1  1 2
--------+-----+-----------+-------------+--------
. x . . |   2 | 192  *  * |  1  1  1  0 |  1  1 1
. . x . |   2 |   * 96  * |  0  2  0  1 |  1  0 2
. . . x |   2 |   *  * 96 |  0  0  2  1 |  0  1 2
--------+-----+-----------+-------------+--------
o3x . . |   3 |   3  0  0 | 64  *  *  * |  1  1 0
. x3x . |   6 |   3  3  0 |  * 64  *  * |  1  0 1
. x . x |   4 |   2  0  2 |  *  * 96  * |  0  1 1
. . x4x |   8 |   0  4  4 |  *  *  * 24 |  0  0 2
--------+-----+-----------+-------------+--------
o3x3x . ♦  12 |  12  6  0 |  4  4  0  0 | 16  * *
o3x . x ♦   6 |   6  0  3 |  2  0  3  0 |  * 32 *
. x3x4x ♦  48 |  24 24 24 |  0  8 12  6 |  *  * 8
x3x3x4x - gidpith
. . . . | 384 |   1   1   1   1 |  1  1  1  1  1  1 |  1  1  1 1
--------+-----+-----------------+-------------------+-----------
x . . . |   2 | 192   *   *   * |  1  1  1  0  0  0 |  1  1  1 0
. x . . |   2 |   * 192   *   * |  1  0  0  1  1  0 |  1  1  0 1
. . x . |   2 |   *   * 192   * |  0  1  0  1  0  1 |  1  0  1 1
. . . x |   2 |   *   *   * 192 |  0  0  1  0  1  1 |  0  1  1 1
--------+-----+-----------------+-------------------+-----------
x3x . . |   6 |   3   3   0   0 | 64  *  *  *  *  * |  1  1  0 0
x . x . |   4 |   2   0   2   0 |  * 96  *  *  *  * |  1  0  1 0
x . . x |   4 |   2   0   0   2 |  *  * 96  *  *  * |  0  1  1 0
. x3x . |   6 |   0   3   3   0 |  *  *  * 64  *  * |  1  0  0 1
. x . x |   4 |   0   2   0   2 |  *  *  *  * 96  * |  0  1  0 1
. . x4x |   8 |   0   0   4   4 |  *  *  *  *  * 48 |  0  0  1 1
--------+-----+-----------------+-------------------+-----------
x3x3x . ♦  24 |  12  12  12   0 |  4  6  0  4  0  0 | 16  *  * *
x3x . x ♦  12 |   6   6   0   6 |  2  0  3  0  3  0 |  * 32  * *
x . x4x ♦  16 |   8   0   8   8 |  0  4  4  0  0  2 |  *  * 24 *
. x3x4x ♦  48 |   0  24  24  24 |  0  0  0  8 12  6 |  *  *  * 8
F4 family
o3x4o3o - rico
. . . . | 96 ♦   6 |  3   6 |  3  2
--------+----+-----+--------+------
. x . . |  2 | 288 |  1   2 |  2  1
--------+----+-----+--------+------
o3x . . |  3 |   3 | 96   * |  2  0
. x4o . |  4 |   4 |  * 144 |  1  1
--------+----+-----+--------+------
o3x4o . ♦ 12 |  24 |  8   6 | 24  *
. x4o3o ♦  8 |  12 |  0   6 |  * 24
x3x4o3o - tico
. . . . | 192 |  1   3 |  3   3 |  3  1
--------+-----+--------+--------+------
x . . . |   2 | 96   * |  3   0 |  3  0
. x . . |   2 |  * 288 |  1   2 |  2  1
--------+-----+--------+--------+------
x3x . . |   6 |  3   3 | 96   * |  2  0
. x4o . |   4 |  0   4 |  * 144 |  1  1
--------+-----+--------+--------+------
x3x4o . ♦  24 | 12  24 |  8   6 | 24  *
. x4o3o ♦   8 |  0  12 |  0   6 |  * 24
x3o4x3o - srico
. . . . | 288 |   2   4 |  1   4   2   2 |  2  2  1
--------+-----+---------+----------------+---------
x . . . |   2 | 288   * |  1   2   0   0 |  2  1  0
. . x . |   2 |   * 576 |  0   1   1   1 |  1  1  1
--------+-----+---------+----------------+---------
x3o . . |   3 |   3   0 | 96   *   *   * |  2  0  0
x . x . |   4 |   2   2 |  * 288   *   * |  1  1  0
. o4x . |   4 |   0   4 |  *   * 144   * |  1  0  1
. . x3o |   3 |   0   3 |  *   *   * 192 |  0  1  1
--------+-----+---------+----------------+---------
x3o4x . ♦  24 |  24  24 |  8  12   6   0 | 24  *  *
x . x3o ♦   6 |   3   6 |  0   3   0   2 |  * 96  *
. o4x3o ♦  12 |   0  24 |  0   0   6   8 |  *  * 24
x3o4o3x - spic
. . . . | 144 ♦   4   4 |   4   8   4 |  1  4  4  1
--------+-----+---------+-------------+------------
x . . . |   2 | 288   * |   2   2   0 |  1  2  1  0
. . . x |   2 |   * 288 |   0   2   2 |  0  1  2  1
--------+-----+---------+-------------+------------
x3o . . |   3 |   3   0 | 192   *   * |  1  1  0  0
x . . x |   4 |   2   2 |   * 288   * |  0  1  1  0
. . o3x |   3 |   0   3 |   *   * 192 |  0  0  1  1
--------+-----+---------+-------------+------------
x3o4o . ♦   6 |  12   0 |   8   0   0 | 24  *  *  *
x3o . x ♦   6 |   6   3 |   2   3   0 |  * 96  *  *
x . o3x ♦   6 |   3   6 |   0   3   2 |  *  * 96  *
. o4o3x ♦   6 |   0  12 |   0   0   8 |  *  *  * 24
o3x4x3o - cont
. . . . | 288 |   2   2 |  1   4  1 |  2  2
--------+-----+---------+-----------+------
. x . . |   2 | 288   * |  1   2  0 |  2  1
. . x . |   2 |   * 288 |  0   2  1 |  1  2
--------+-----+---------+-----------+------
o3x . . |   3 |   3   0 | 96   *  * |  2  0
. x4x . |   8 |   4   4 |  * 144  * |  1  1
. . x3o |   3 |   0   3 |  *   * 96 |  0  2
--------+-----+---------+-----------+------
o3x4x . ♦  24 |  24  12 |  8   6  0 | 24  *
. x4x3o ♦  24 |  12  24 |  0   6  8 |  * 24
x3x4x3o - grico
. . . . | 576 |   1   1   2 |  1   2   2   1 |  2  1  1
--------+-----+-------------+----------------+---------
x . . . |   2 | 288   *   * |  1   2   0   0 |  2  1  0
. x . . |   2 |   * 288   * |  1   0   2   0 |  2  0  1
. . x . |   2 |   *   * 576 |  0   1   1   1 |  1  1  1
--------+-----+-------------+----------------+---------
x3x . . |   6 |   3   3   0 | 96   *   *   * |  2  0  0
x . x . |   4 |   2   0   2 |  * 288   *   * |  1  1  0
. x4x . |   8 |   0   4   4 |  *   * 144   * |  1  0  1
. . x3o |   3 |   0   0   3 |  *   *   * 192 |  0  1  1
--------+-----+-------------+----------------+---------
x3x4x . ♦  48 |  24  24  24 |  8  12   6   0 | 24  *  *
x . x3o ♦   6 |   3   0   6 |  0   3   0   2 |  * 96  *
. x4x3o ♦  24 |   0  12  24 |  0   0   6   8 |  *  * 24
x3x4o3x - prico
. . . . | 576 |   1   2   2 |   2   2   1   2   1 |  1  2  1  1
--------+-----+-------------+---------------------+------------
x . . . |   2 | 288   *   * |   2   2   0   0   0 |  1  2  1  0
. x . . |   2 |   * 576   * |   1   0   1   1   0 |  1  1  0  1
. . . x |   2 |   *   * 576 |   0   1   0   1   1 |  0  1  1  1
--------+-----+-------------+---------------------+------------
x3x . . |   6 |   3   3   0 | 192   *   *   *   * |  1  1  0  0
x . . x |   4 |   2   0   2 |   * 288   *   *   * |  0  1  1  0
. x4o . |   4 |   0   4   0 |   *   * 144   *   * |  1  0  0  1
. x . x |   4 |   0   2   2 |   *   *   * 288   * |  0  1  0  1
. . o3x |   3 |   0   0   3 |   *   *   *   * 192 |  0  0  1  1
--------+-----+-------------+---------------------+------------
x3x4o . ♦  24 |  12  24   0 |   8   0   6   0   0 | 24  *  *  *
x3x . x ♦  12 |   6   6   6 |   2   3   0   3   0 |  * 96  *  *
x . o3x ♦   6 |   3   0   6 |   0   3   0   0   2 |  *  * 96  *
. x4o3x ♦  24 |   0  24  24 |   0   0   6  12   8 |  *  *  * 24
x3x4x3x - gippic
. . . . | 1152 |   1   1   1   1 |   1   1   1   1   1   1 |  1  1  1  1
--------+------+-----------------+-------------------------+------------
x . . . |    2 | 576   *   *   * |   1   1   1   0   0   0 |  1  1  1  0
. x . . |    2 |   * 576   *   * |   1   0   0   1   1   0 |  1  1  0  1
. . x . |    2 |   *   * 576   * |   0   1   0   1   0   1 |  1  0  1  1
. . . x |    2 |   *   *   * 576 |   0   0   1   0   1   1 |  0  1  1  1
--------+------+-----------------+-------------------------+------------
x3x . . |    6 |   3   3   0   0 | 192   *   *   *   *   * |  1  1  0  0
x . x . |    4 |   2   0   2   0 |   * 288   *   *   *   * |  1  0  1  0
x . . x |    4 |   2   0   0   2 |   *   * 288   *   *   * |  0  1  1  0
. x4x . |    8 |   0   4   4   0 |   *   *   * 144   *   * |  1  0  0  1
. x . x |    4 |   0   2   0   2 |   *   *   *   * 288   * |  0  1  0  1
. . x3x |    6 |   0   0   3   3 |   *   *   *   *   * 192 |  0  0  1  1
--------+------+-----------------+-------------------------+------------
x3x4x . ♦   48 |  24  24  24   0 |   8  12   0   6   0   0 | 24  *  *  *
x3x . x ♦   12 |   6   6   0   6 |   2   0   3   0   3   0 |  * 96  *  *
x . x3x ♦   12 |   6   0   6   6 |   0   3   3   0   0   2 |  *  * 96  *
. x4x3x ♦   48 |   0  24  24  24 |   0   0   0   6  12   8 |  *  *  * 24
s3s4o3o - sadi
demi( . . . . ) | 96 ♦   3   6 |  3   9  3 |  3  1  4
----------------+----+---------+-----------+---------
      . s4o .   |  2 | 144   * |  0   2  2 |  1  1  2
sefa( s3s . . ) |  2 |   * 288 |  1   2  0 |  2  0  1
----------------+----+---------+-----------+---------
      s3s . .   ♦  3 |   0   3 | 96   *  * |  2  0  0
sefa( s3s4o . ) |  3 |   1   2 |  * 288  * |  1  0  1
sefa( . s4o3o ) |  3 |   3   0 |  *   * 96 |  0  1  1
----------------+----+---------+-----------+---------
      s3s4o .   ♦ 12 |   6  24 |  8  12  0 | 24  *  *
      . s4o3o   ♦  4 |   6   0 |  0   0  4 |  * 24  *
sefa( s3s4o3o ) ♦  4 |   3   3 |  0   3  1 |  *  * 96
H4 family
o3x3o5o - rox
. . . . | 720 ♦   10 |    5   10 |   5   2
--------+-----+------+-----------+--------
. x . . |   2 | 3600 |    1    2 |   2   1
--------+-----+------+-----------+--------
o3x . . |   3 |    3 | 1200    * |   2   0
. x3o . |   3 |    3 |    * 2400 |   1   1
--------+-----+------+-----------+--------
o3x3o . ♦   6 |   12 |    4    4 | 600   *
. x3o5o ♦  12 |   30 |    0   20 |   * 120
o3o3x5o - rahi
. . . . | 1200 ♦    6 |    6   3 |   2   3
--------+------+------+----------+--------
. . x . |    2 | 3600 |    2   1 |   1   2
--------+------+------+----------+--------
. o3x . |    3 |    3 | 2400   * |   1   1
. . x5o |    5 |    5 |    * 720 |   0   2
--------+------+------+----------+--------
o3o3x . ♦    4 |    6 |    4   0 | 600   *
. o3x5o ♦   30 |   60 |   20  12 |   * 120
x3x3o5o - tex
. . . . | 1440 |   1    5 |    5    5 |   5   1
--------+------+----------+-----------+--------
x . . . |    2 | 720    * |    5    0 |   5   0
. x . . |    2 |   * 3600 |    1    2 |   2   1
--------+------+----------+-----------+--------
x3x . . |    6 |   3    3 | 1200    * |   2   0
. x3o . |    3 |   0    3 |    * 2400 |   1   1
--------+------+----------+-----------+--------
x3x3o . ♦   12 |   6   12 |    4    4 | 600   *
. x3o5o ♦   12 |   0   30 |    0   20 |   * 120
x3o3x5o - srix
. . . . | 3600 |    2    4 |    1    4    2    2 |   2   2   1
--------+------+-----------+---------------------+------------
x . . . |    2 | 3600    * |    1    2    0    0 |   2   1   0
. . x . |    2 |    * 7200 |    0    1    1    1 |   1   1   1
--------+------+-----------+---------------------+------------
x3o . . |    3 |    3    0 | 1200    *    *    * |   2   0   0
x . x . |    4 |    2    2 |    * 3600    *    * |   1   1   0
. o3x . |    3 |    0    3 |    *    * 2400    * |   1   0   1
. . x5o |    5 |    0    5 |    *    *    * 1440 |   0   1   1
--------+------+-----------+---------------------+------------
x3o3x . ♦   12 |   12   12 |    4    6    4    0 | 600   *   *
x . x5o ♦   10 |    5   10 |    0    5    0    2 |   * 720   *
. o3x5o ♦   30 |    0   60 |    0    0   20   12 |   *   * 120
x3o3o5x - sidpixhi
. . . . | 2400 |    3    3 |    3    6    3 |   1    3   3   1
--------+------+-----------+----------------+-----------------
x . . . |    2 | 3600    * |    2    2    0 |   1    2   1   0
. . . x |    2 |    * 3600 |    0    2    2 |   0    1   2   1
--------+------+-----------+----------------+-----------------
x3o . . |    3 |    3    0 | 2400    *    * |   1    1   0   0
x . . x |    4 |    2    2 |    * 3600    * |   0    1   1   0
. . o5x |    5 |    0    5 |    *    * 1440 |   0    0   1   1
--------+------+-----------+----------------+-----------------
x3o3o . ♦    4 |    6    0 |    4    0    0 | 600    *   *   *
x3o . x ♦    6 |    6    3 |    2    3    0 |   * 1200   *   *
x . o5x ♦   10 |    5   10 |    0    5    2 |   *    * 720   *
. o3o5x ♦   20 |    0   30 |    0    0   12 |   *    *   * 120
o3x3x5o - xhi
. . . . | 3600 |    2    2 |    1    4   1 |   2   2
--------+------+-----------+---------------+--------
. x . . |    2 | 3600    * |    1    2   0 |   2   1
. . x . |    2 |    * 3600 |    0    2   1 |   1   2
--------+------+-----------+---------------+--------
o3x . . |    3 |    3    0 | 1200    *   * |   2   0
. x3x . |    6 |    3    3 |    * 2400   * |   1   1
. . x5o |    5 |    0    5 |    *    * 720 |   0   2
--------+------+-----------+---------------+--------
o3x3x . ♦   12 |   12    6 |    4    4   0 | 600   *
. x3x5o ♦   60 |   30   60 |    0   20  12 |   * 120
o3x3o5x - srahi
. . . . | 3600 |    4    2 |    2    2    4   1 |   1    2   2
--------+------+-----------+--------------------+-------------
. x . . |    2 | 7200    * |    1    1    1   0 |   1    1   1
. . . x |    2 |    * 3600 |    0    0    2   1 |   0    1   2
--------+------+-----------+--------------------+-------------
o3x . . |    3 |    3    0 | 2400    *    *   * |   1    1   0
. x3o . |    3 |    3    0 |    * 2400    *   * |   1    0   1
. x . x |    4 |    2    2 |    *    * 3600   * |   0    1   1
. . o5x |    5 |    0    5 |    *    *    * 720 |   0    0   2
--------+------+-----------+--------------------+-------------
o3x3o . ♦    6 |   12    0 |    4    4    0   0 | 600    *   *
o3x . x ♦    6 |    6    3 |    2    0    3   0 |   * 1200   *
. x3o5x ♦   60 |   60   60 |    0   20   30  12 |   *    * 120
o3o3x5x - thi
. . . . | 2400 |    3    1 |    3   3 |   1   3
--------+------+-----------+----------+--------
. . x . |    2 | 3600    * |    2   1 |   1   2
. . . x |    2 |    * 1200 |    0   3 |   0   3
--------+------+-----------+----------+--------
. o3x . |    3 |    3    0 | 2400   * |   1   1
. . x5x |   10 |    5    5 |    * 720 |   0   2
--------+------+-----------+----------+--------
o3o3x . ♦    4 |    6    0 |    4   0 | 600   *
. o3x5x ♦   60 |   60   30 |   20  12 |   * 120
x3x3x5o - grix
. . . . | 7200 |    1    1    2 |    1    2    2    1 |   2   1   1
--------+------+----------------+---------------------+------------
x . . . |    2 | 3600    *    * |    1    2    0    0 |   2   1   0
. x . . |    2 |    * 3600    * |    1    0    2    0 |   2   0   1
. . x . |    2 |    *    * 7200 |    0    1    1    1 |   1   1   1
--------+------+----------------+---------------------+------------
x3x . . |    6 |    3    3    0 | 1200    *    *    * |   2   0   0
x . x . |    4 |    2    0    2 |    * 3600    *    * |   1   1   0
. x3x . |    6 |    0    3    3 |    *    * 2400    * |   1   0   1
. . x5o |    5 |    0    0    5 |    *    *    * 1440 |   0   1   1
--------+------+----------------+---------------------+------------
x3x3x . ♦   24 |   12   12   12 |    4    6    4    0 | 600   *   *
x . x5o ♦   10 |    5    0   10 |    0    5    0    2 |   * 720   *
. x3x5o ♦   60 |    0   30   60 |    0    0   20   12 |   *   * 120
x3x3o5x - prahi
. . . . | 7200 |    1    2    2 |    2    2    1    2    1 |   1    2   1   1
--------+------+----------------+--------------------------+-----------------
x . . . |    2 | 3600    *    * |    2    2    0    0    0 |   1    2   1   0
. x . . |    2 |    * 7200    * |    1    0    1    1    0 |   1    1   0   1
. . . x |    2 |    *    * 7200 |    0    1    0    1    1 |   0    1   1   1
--------+------+----------------+--------------------------+-----------------
x3x . . |    6 |    3    3    0 | 2400    *    *    *    * |   1    1   0   0
x . . x |    4 |    2    0    2 |    * 3600    *    *    * |   0    1   1   0
. x3o . |    3 |    0    3    0 |    *    * 2400    *    * |   1    0   0   1
. x . x |    4 |    0    2    2 |    *    *    * 3600    * |   0    1   0   1
. . o5x |    5 |    0    0    5 |    *    *    *    * 1440 |   0    0   1   1
--------+------+----------------+--------------------------+-----------------
x3x3o . ♦   12 |    6   12    0 |    4    0    4    0    0 | 600    *   *   *
x3x . x ♦   12 |    6    6    6 |    2    3    0    3    0 |   * 1200   *   *
x . o5x ♦   10 |    5    0   10 |    0    5    0    0    2 |   *    * 720   *
. x3o5x ♦   60 |    0   60   60 |    0    0   20   30   12 |   *    *   * 120
x3o3x5x - prix
. . . . | 7200 |    2    2    1 |    1    2    2    1    2 |   1    1   2   1
--------+------+----------------+--------------------------+-----------------
x . . . |    2 | 7200    *    * |    1    1    1    0    0 |   1    1   1   0
. . x . |    2 |    * 7200    * |    0    1    0    1    1 |   1    0   1   1
. . . x |    2 |    *    * 3600 |    0    0    2    0    2 |   0    1   2   1
--------+------+----------------+--------------------------+-----------------
x3o . . |    3 |    3    0    0 | 2400    *    *    *    * |   1    1   0   0
x . x . |    4 |    2    2    0 |    * 3600    *    *    * |   1    0   1   0
x . . x |    4 |    2    0    2 |    *    * 3600    *    * |   0    1   1   0
. o3x . |    3 |    0    3    0 |    *    *    * 2400    * |   1    0   0   1
. . x5x |   10 |    0    5    5 |    *    *    *    * 1440 |   0    0   1   1
--------+------+----------------+--------------------------+-----------------
x3o3x . ♦   12 |   12   12    0 |    4    6    0    4    0 | 600    *   *   *
x3o . x ♦    6 |   12    0    6 |    2    0    3    0    0 |   * 1200   *   *
x . x5x ♦   20 |   10   10   10 |    0    5    5    0    2 |   *    * 720   *
. o3x5x ♦   60 |    0   60   30 |    0    0    0   20   12 |   *    *   * 120
o3x3x5x - grahi
. . . . | 7200 |    2    1    1 |    1    2    2   1 |   1    1   2
--------+------+----------------+--------------------+-------------
. x . . |    2 | 7200    *    * |    1    1    1   0 |   1    1   1
. . x . |    2 |    * 3600    * |    0    2    0   1 |   1    0   2
. . . x |    2 |    *    * 3600 |    0    0    2   1 |   0    1   2
--------+------+----------------+--------------------+-------------
o3x . . |    3 |    3    0    0 | 2400    *    *   * |   1    1   0
. x3x . |    6 |    3    3    0 |    * 2400    *   * |   1    0   1
. x . x |    4 |    2    0    2 |    *    * 3600   * |   0    1   1
. . x5x |   10 |    0    5    5 |    *    *    * 720 |   0    0   2
--------+------+----------------+--------------------+-------------
o3x3x . ♦   12 |   12    6    0 |    4    4    0   0 | 600    *   *
o3x . x ♦    6 |    6    0    3 |    2    0    3   0 |   * 1200   *
. x3x5x ♦  120 |   60   60   60 |    0   20   30  12 |   *    * 120
x3x3x5x - gidpixhi

. . . . | 14400 |    1    1    1    1 |    1    1    1    1    1    1 |   1    1   1   1
--------+-------+---------------------+-------------------------------+-----------------
x . . . |     2 | 7200    *    *    * |    1    1    1    0    0    0 |   1    1   1   0
. x . . |     2 |    * 7200    *    * |    1    0    0    1    1    0 |   1    1   0   1
. . x . |     2 |    *    * 7200    * |    0    1    0    1    0    1 |   1    0   1   1
. . . x |     1 |    *    *    * 7200 |    0    0    1    0    1    1 |   0    1   1   1
--------+-------+---------------------+-------------------------------+-----------------
x3x . . |     6 |    3    3    0    0 | 2400    *    *    *    *    * |   1    1   0   0
x . x . |     4 |    2    0    2    0 |    * 3600    *    *    *    * |   1    0   1   0
x . . x |     4 |    2    0    0    2 |    *    * 3600    *    *    * |   0    1   1   0
. x3x . |     6 |    0    3    3    0 |    *    *    * 2400    *    * |   1    0   0   1
. x . x |     4 |    0    2    0    2 |    *    *    *    * 3600    * |   0    1   0   1
. . x5x |    10 |    0    0    5    5 |    *    *    *    *    * 1440 |   0    0   1   1
--------+-------+---------------------+-------------------------------+-----------------
x3x3x . ♦    24 |   12   12   12    0 |    4    6    0    4    0    0 | 600    *   *   *
x3x . x ♦    12 |    6    6    0    6 |    2    0    3    0    3    0 |   * 1200   *   *
x . x5x ♦    20 |   10    0   10   10 |    0    5    5    0    0    2 |   *    * 720   *
. x3x5x ♦   120 |    0   60   60   60 |    0    0    0   20   30   12 |   *    *   * 120

5D[edit]

5D
5-simplex {3,3,3,3} [46] 5-orthoplex {3,3,3,4} [47] 5-cube {4,3,3,3} [48]
x3o3o3o3o
. . . . . | 6 ♦  5 | 10 | 10 | 5
----------+---+----+----+----+--
x . . . . | 2 | 15 ♦  4 |  6 | 4
----------+---+----+----+----+--
x3o . . . | 3 |  3 | 20 |  3 | 3
----------+---+----+----+----+--
x3o3o . . ♦ 4 |  6 |  4 | 15 | 2
----------+---+----+----+----+--
x3o3o3o . ♦ 5 | 10 | 10 |  5 | 6
x3o3o3o4o
. . . . . | 10 ♦  8 | 24 | 32 | 16
----------+----+----+----+----+---
x . . . . |  2 | 40 ♦  6 | 12 |  8
----------+----+----+----+----+---
x3o . . . |  3 |  3 | 80 |  4 |  4
----------+----+----+----+----+---
x3o3o . . ♦  4 |  6 |  4 | 80 |  2
----------+----+----+----+----+---
x3o3o3o . ♦  5 | 10 | 10 |  5 | 32
o3o3o3o4x
. . . . . | 32 ♦  5 | 10 | 10 |  5
----------+----+----+----+----+---
. . . . x |  2 | 80 ♦  4 |  6 |  4
----------+----+----+----+----+---
. . . o4x |  4 |  4 | 80 |  3 |  3
----------+----+----+----+----+---
. . o3o4x ♦  8 | 12 |  6 | 40 |  2
----------+----+----+----+----+---
. o3o3o4x ♦ 16 | 32 | 24 |  8 | 10

5-simplexes[edit]

5D
5-simplex {3,3,3,3} [49]
x3o3o3o3o
. . . . . | 6 ♦  5 | 10 | 10 | 5
----------+---+----+----+----+--
x . . . . | 2 | 15 ♦  4 |  6 | 4
----------+---+----+----+----+--
x3o . . . | 3 |  3 | 20 |  3 | 3
----------+---+----+----+----+--
x3o3o . . ♦ 4 |  6 |  4 | 15 | 2
----------+---+----+----+----+--
x3o3o3o . ♦ 5 | 10 | 10 |  5 | 6
(pt || pen)
o.3o.3o.3o.    | 1 * ♦ 5  0 | 10  0 | 10 0 | 5 0
.o3.o3.o3.o    | * 5 ♦ 1  4 |  4  6 |  6 4 | 4 1
---------------+-----+------+-------+------+----
oo3oo3oo3oo&#x | 1 1 | 5  * ♦  4  0 |  6 0 | 4 0
.x .. .. ..    | 0 2 | * 10 ♦  1  3 |  3 3 | 3 1
---------------+-----+------+-------+------+----
ox .. .. ..&#x | 1 2 | 2  1 | 10  * |  3 0 | 3 0
.x3.o .. ..    | 0 3 | 0  3 |  * 10 |  1 2 | 2 1
---------------+-----+------+-------+------+----
ox3oo .. ..&#x ♦ 1 3 | 3  3 |  3  1 | 10 * | 2 0
.x3.o3.o ..    ♦ 0 4 | 0  6 |  0  4 |  * 5 | 1 1
---------------+-----+------+-------+------+----
ox3oo3oo ..&#x ♦ 1 4 | 4  6 |  6  4 |  4 1 | 5 *
.x3.o3.o3.o    ♦ 0 5 | 0 10 |  0 10 |  0 5 | * 1
(line || perp tet)
o. o.3o.3o.    | 2 * ♦ 1 4 0 | 4  6 0 | 6 4 0 | 4 1
.o .o3.o3.o    | * 4 ♦ 0 2 3 | 1  6 3 | 3 6 1 | 3 2
---------------+-----+-------+--------+-------+----
x. .. .. ..    | 2 0 | 1 * * ♦ 4  0 0 | 6 0 0 | 4 0
oo oo3oo3oo&#x | 1 1 | * 8 * ♦ 1  3 0 | 3 3 0 | 3 1
.. .x .. ..    | 0 2 | * * 6 ♦ 0  2 2 | 1 4 1 | 2 2
---------------+-----+-------+--------+-------+----
xo .. .. ..&#x | 2 1 | 1 2 0 | 4  * * | 3 0 0 | 3 0
.. ox .. ..&#x | 1 2 | 0 2 1 | * 12 * | 1 2 0 | 2 1
.. .x3.o ..    | 0 3 | 0 0 3 | *  * 4 | 0 2 1 | 1 2
---------------+-----+-------+--------+-------+----
xo ox .. ..&#x ♦ 2 2 | 1 4 1 | 2  2 0 | 6 * * | 2 0
.. ox3oo ..&#x ♦ 1 3 | 0 3 3 | 0  3 1 | * 8 * | 1 1
.. .x3.o3.o    ♦ 0 4 | 0 0 6 | 0  0 4 | * * 1 | 0 2
---------------+-----+-------+--------+-------+----
xo ox3oo ..&#x ♦ 2 3 | 1 6 3 | 3  6 1 | 3 2 0 | 4 *
.. ox3oo3oo&#x ♦ 1 4 | 0 4 6 | 0  6 4 | 0 4 1 | * 2
({3} || perp {3})
o.3o. o.3o.    & | 6 ♦ 2 3 | 1  9 | 4 3 | 5
-----------------+---+-----+------+-----+--
x. .. .. ..    & | 2 | 6 * ♦ 1  3 | 3 3 | 4
oo3oo oo3oo&#x   | 2 | * 9 ♦ 0  4 | 2 4 | 4
-----------------+---+-----+------+-----+--
x.3o. .. ..    & | 3 | 3 0 | 2  * | 3 0 | 3
xo .. .. ..&#x & | 3 | 1 2 | * 18 | 1 2 | 3
-----------------+---+-----+------+-----+--
xo3oo .. ..&#x & ♦ 4 | 3 3 | 1  3 | 6 * | 2
xo .. ox ..&#x   ♦ 4 | 2 4 | 0  4 | * 9 | 2
-----------------+---+-----+------+-----+--
xo3oo ox ..&#x & ♦ 5 | 4 6 | 1  9 | 2 3 | 6
 
o..3o..3o..    | 1 * * ♦ 4 1 0 0 | 6 4 0 0 | 4 6 0 0 | 1 4 0
.o.3.o.3.o.    | * 4 * ♦ 1 0 3 1 | 3 1 3 3 | 3 3 1 3 | 1 3 1
..o3..o3..o    | * * 1 ♦ 0 1 0 4 | 0 4 0 6 | 0 6 0 4 | 0 4 1
---------------+-------+---------+---------+---------+------
oo.3oo.3oo.&#x | 1 1 0 | 4 * * * ♦ 3 1 0 0 | 3 3 0 0 | 1 3 0
o.o3o.o3o.o&#x | 1 0 1 | * 1 * * ♦ 0 4 0 0 | 0 6 0 0 | 0 4 0
.x. ... ...    | 0 2 0 | * * 6 * ♦ 1 0 2 1 | 2 1 1 2 | 1 2 1
.oo3.oo3.oo&#x | 0 1 1 | * * * 4 ♦ 0 1 0 3 | 0 3 0 3 | 0 3 1
---------------+-------+---------+---------+---------+------
ox. ... ...&#x | 1 2 0 | 2 0 1 0 | 6 * * * | 2 1 0 0 | 1 2 0
ooo3ooo3ooo&#x | 1 1 1 | 1 1 0 1 | * 4 * * | 0 3 0 0 | 0 3 0
.x.3.o. ...    | 0 3 0 | 0 0 3 0 | * * 4 * | 1 0 1 1 | 1 1 1
.xo ... ...&#x | 0 2 1 | 0 0 1 2 | * * * 6 | 0 1 0 2 | 0 2 1
---------------+-------+---------+---------+---------+------
ox.3oo. ...&#x ♦ 1 3 0 | 3 0 3 0 | 3 0 1 0 | 4 * * * | 1 1 0
oxo ... ...&#x ♦ 1 2 1 | 2 1 1 2 | 1 2 0 1 | * 6 * * | 0 2 0
.x.3.o.3.o.    ♦ 0 4 0 | 0 0 6 0 | 0 0 4 0 | * * 1 * | 1 0 1
.xo3.oo ...&#x ♦ 0 3 1 | 0 0 3 3 | 0 0 1 3 | * * * 4 | 0 1 1
---------------+-------+---------+---------+---------+------
ox.3oo.3oo.&#x ♦ 1 4 0 | 4 0 6 0 | 6 0 4 0 | 4 0 1 0 | 1 * *
oxo3ooo ...&#x ♦ 1 3 1 | 3 1 3 3 | 3 3 1 3 | 1 3 0 1 | * 4 *
.xo3.oo3.oo&#x ♦ 0 4 1 | 0 0 6 4 | 0 0 4 6 | 0 0 1 4 | * * 1
( (pt || {3}) || line )
o..3o.. o..    | 1 * * ♦ 3 2 0 0 0 | 3 1 6 0 0 0 | 1 6 3 0 0 | 2 3 0
.o.3.o. .o.    | * 3 * ♦ 1 0 2 2 0 | 2 0 2 1 4 1 | 1 4 1 2 2 | 2 2 1
..o3..o ..o    | * * 2 ♦ 0 1 0 3 1 | 0 1 3 0 3 3 | 0 3 3 1 3 | 1 3 1
---------------+-------+-----------+-------------+-----------+------
oo.3oo. oo.&#x | 1 1 0 | 3 * * * * ♦ 2 0 2 0 0 0 | 1 4 1 0 0 | 2 2 0
o.o3o.o o.o&#x | 1 0 1 | * 2 * * * ♦ 0 1 3 0 0 0 | 0 3 3 0 0 | 1 3 0
.x. ... ...    | 0 2 0 | * * 3 * * ♦ 1 0 0 1 2 0 | 1 2 0 2 1 | 2 1 1
.oo3.oo .oo&#x | 0 1 1 | * * * 6 * ♦ 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
... ... ..x    | 0 0 2 | * * * * 1 ♦ 0 1 0 0 0 3 | 0 0 3 0 3 | 0 3 1
---------------+-------+-----------+-------------+-----------+------
ox. ... ...&#x | 1 2 0 | 2 0 1 0 0 | 3 * * * * * | 1 2 0 0 0 | 2 1 0
... ... o.x&#x | 1 0 2 | 0 2 0 0 1 | * 1 * * * * | 0 0 3 0 0 | 0 3 0
ooo3ooo ooo&#x | 1 1 1 | 1 1 0 1 0 | * * 6 * * * | 0 2 1 0 0 | 1 2 0
.x.3.o. ...    | 0 3 0 | 0 0 3 0 0 | * * * 1 * * | 1 0 0 2 0 | 2 0 1
.xo ... ...&#x | 0 2 1 | 0 0 1 2 0 | * * * * 6 * | 0 1 0 1 1 | 1 1 1
... ... .ox&#x | 0 1 2 | 0 0 0 2 1 | * * * * * 3 | 0 0 1 0 2 | 0 2 1
---------------+-------+-----------+-------------+-----------+------
ox.3oo. ...&#x ♦ 1 3 0 | 3 0 3 0 0 | 3 0 0 1 0 0 | 1 * * * * | 2 0 0
oxo ... ...&#x ♦ 1 2 1 | 2 1 1 2 0 | 1 0 2 0 1 0 | * 6 * * * | 1 1 0
... ... oox&#x ♦ 1 1 2 | 1 2 0 2 1 | 0 1 2 0 0 1 | * * 3 * * | 0 2 0
.xo3.oo ...&#x ♦ 0 3 1 | 0 0 3 3 0 | 0 0 0 1 3 0 | * * * 2 * | 1 0 1
.xo ... .ox&#x ♦ 0 2 2 | 0 0 1 4 1 | 0 0 0 0 2 2 | * * * * 3 | 0 1 1
---------------+-------+-----------+-------------+-----------+------
oxo3ooo ...&#x ♦ 1 3 1 | 3 1 3 3 0 | 3 0 3 1 3 0 | 1 3 0 1 0 | 2 * *
oxo ... oox&#x ♦ 1 2 2 | 2 2 1 4 1 | 1 1 4 0 2 2 | 0 2 2 0 1 | * 3 *
.xo3.oo .ox&#x ♦ 0 3 2 | 0 0 3 6 1 | 0 0 0 1 6 3 | 0 0 0 2 3 | * * 1
( (line || perp line) || perp line)
o.. o.. o..    | 2 * * ♦ 1 2 2 0 0 0 | 2 2 1 1 4 0 0 | 4 1 1 2 2 0 | 2 2 1
.o. .o. .o.    | * 2 * ♦ 0 2 0 1 2 0 | 1 0 2 0 4 2 1 | 2 1 0 4 2 1 | 2 1 2
..o ..o ..o    | * * 2 ♦ 0 0 2 0 2 1 | 0 1 0 2 4 1 2 | 2 0 1 2 4 1 | 1 2 2
---------------+-------+-------------+---------------+-------------+------
x.. ... ...    | 2 0 0 | 1 * * * * * ♦ 2 2 0 0 0 0 0 | 4 1 1 0 0 0 | 2 2 0
oo. oo. oo.&#x | 1 1 0 | * 4 * * * * ♦ 1 0 1 0 2 0 0 | 2 1 0 2 1 0 | 2 1 1
o.o o.o o.o&#x | 1 0 1 | * * 4 * * * ♦ 0 1 0 1 2 0 0 | 2 0 1 1 2 0 | 1 2 1
... .x. ...    | 0 2 0 | * * * 1 * * ♦ 0 0 2 0 0 2 0 | 0 1 0 4 0 1 | 2 0 2
.oo .oo .oo&#x | 0 1 1 | * * * * 4 * ♦ 0 0 0 0 2 1 1 | 1 0 0 2 2 1 | 1 1 2
... ... ..x    | 0 0 2 | * * * * * 1 ♦ 0 0 0 2 0 0 2 | 0 0 1 0 4 1 | 0 2 2
---------------+-------+-------------+---------------+-------------+------
xo. ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | 2 * * * * * * | 2 1 0 0 0 0 | 2 1 0
x.o ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * 2 * * * * * | 2 0 1 0 0 0 | 1 2 0
... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 | * * 2 * * * * | 0 1 0 2 0 0 | 2 0 1
... ... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * 2 * * * | 0 0 1 0 2 0 | 0 2 1
ooo ooo ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * 8 * * | 1 0 0 1 1 0 | 1 1 1
... .xo ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * 2 * | 0 0 0 2 0 1 | 1 0 2
... ... .ox&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * 2 | 0 0 0 0 2 1 | 0 1 2
---------------+-------+-------------+---------------+-------------+------
xoo ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 1 1 0 0 2 0 0 | 4 * * * * * | 1 1 0
xo. ox. ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 2 0 2 0 0 0 0 | * 1 * * * * | 2 0 0
x.o ... o.x&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 2 0 2 0 0 0 | * * 1 * * * | 0 2 0
... oxo ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 0 1 0 2 1 0 | * * * 4 * * | 1 0 1
... ... oox&#x ♦ 1 1 2 | 0 1 2 0 2 1 | 0 0 0 1 2 0 1 | * * * * 4 * | 0 1 1
... .xo .ox&#x ♦ 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 0 2 2 | * * * * * 1 | 0 0 2
---------------+-------+-------------+---------------+-------------+------
xoo oxo ...&#x ♦ 2 2 1 | 1 4 2 1 2 0 | 2 1 2 0 4 1 0 | 2 1 0 2 0 0 | 2 * *
xoo ... oox&#x ♦ 2 1 2 | 1 2 4 0 2 1 | 1 2 0 2 4 0 1 | 2 0 1 0 2 0 | * 2 *
... oxo oox&#x ♦ 1 2 2 | 0 2 2 1 4 1 | 0 0 1 1 4 2 2 | 0 0 0 2 2 1 | * * 2

Uniform 5D[edit]

5D
5-demicube
h{4,3,3,3}[50]
r{3,3,3,3}[51] 2r{3,3,3,3}[52] 2r{4,3,3,3}[53]
x3o3o *b3o3o - hin
. . .    . . | 16 ♦ 10 |  30 | 10 20 |  5  5
-------------+----+----+-----+-------+------
x . .    . . |  2 | 80 ♦   6 |  3  6 |  3  2
-------------+----+----+-----+-------+------
x3o .    . . |  3 |  3 | 160 |  1  2 |  2  1
-------------+----+----+-----+-------+------
x3o3o    . . ♦  4 |  6 |   4 | 40  * |  2  0
x3o . *b3o . ♦  4 |  6 |   4 |  * 80 |  1  1
-------------+----+----+-----+-------+------
x3o3o *b3o . ♦  8 | 24 |  32 |  8  8 | 10  *
x3o . *b3o3o ♦  5 | 10 |  10 |  0  5 |  * 16
o3x3o3o3o - rix
. . . . . | 15 ♦  8 |  4 12 |  6  8 | 4 2
----------+----+----+-------+-------+----
. x . . . |  2 | 60 |  1  3 |  3  3 | 3 1
----------+----+----+-------+-------+----
o3x . . . |  3 |  3 | 20  * |  3  0 | 3 0
. x3o . . |  3 |  3 |  * 60 |  1  2 | 2 1
----------+----+----+-------+-------+----
o3x3o . . ♦  6 | 12 |  4  4 | 15  * | 2 0
. x3o3o . ♦  4 |  6 |  0  4 |  * 30 | 1 1
----------+----+----+-------+-------+----
o3x3o3o . ♦ 10 | 30 | 10 20 |  5  5 | 6 *
. x3o3o3o ♦  5 | 10 |  0 10 |  0  5 | * 6
o3o3x3o3o - dot
. . . . . | 20 ♦  9 |  9  9 |  3  9  3 | 3 3
----------+----+----+-------+----------+----
. . x . . |  2 | 90 |  2  2 |  1  4  1 | 2 2
----------+----+----+-------+----------+----
. o3x . . |  3 |  3 | 60  * |  1  2  0 | 2 1
. . x3o . |  3 |  3 |  * 60 |  0  2  1 | 1 2
----------+----+----+-------+----------+----
o3o3x . . ♦  4 |  6 |  4  0 | 15  *  * | 2 0
. o3x3o . ♦  6 | 12 |  4  4 |  * 30  * | 1 1
. . x3o3o ♦  4 |  6 |  0  4 |  *  * 15 | 0 2
----------+----+----+-------+----------+----
o3o3x3o . ♦ 10 | 30 | 20 10 |  5  5  0 | 6 *
. o3x3o3o ♦ 10 | 30 | 10 20 |  0  5  5 | * 6
o3x3o *b3o3o - nit
. . .    . . | 80 ♦  12 |   6   6  12 |  3  6  6  4 |  3  2  2
-------------+----+-----+-------------+-------------+---------
. x .    . . |  2 | 480 |   1   1   2 |  1  2  2  1 |  2  1  1
-------------+----+-----+-------------+-------------+---------
o3x .    . . |  3 |   3 | 160   *   * |  1  2  0  0 |  2  1  0
. x3o    . . |  3 |   3 |   * 160   * |  1  0  2  0 |  2  0  1
. x . *b3o . |  3 |   3 |   *   * 320 |  0  1  1  1 |  1  1  1
-------------+----+-----+-------------+-------------+---------
o3x3o    . . ♦  6 |  12 |   4   4   0 | 40  *  *  * |  2  0  0
o3x . *b3o . ♦  6 |  12 |   4   0   4 |  * 80  *  * |  1  1  0
. x3o *b3o . ♦  6 |  12 |   0   4   4 |  *  * 80  * |  1  0  1
. x . *b3o3o ♦  4 |   6 |   0   0   4 |  *  *  * 80 |  0  1  1
-------------+----+-----+-------------+-------------+---------
o3x3o *b3o . ♦ 24 |  96 |  32  32  32 |  8  8  8  0 | 10  *  *
o3x . *b3o3o ♦ 10 |  30 |  10   0  20 |  0  5  0  5 |  * 16  *
. x3o *b3o3o ♦ 10 |  30 |   0  10  20 |  0  0  5  5 |  *  * 16

6D[edit]

6D regular
6-simplex {3,3,3,3,3} [54] 6-orthoplex {3,3,3,3,4} [55] 6-cube {4,3,3,3,3} [56]
x3o3o3o3o3o
. . . . . . | 7 ♦  6 | 15 | 20 | 15 | 6
------------+---+----+----+----+----+--
x . . . . . | 2 | 21 ♦  5 | 10 | 10 | 5
------------+---+----+----+----+----+--
x3o . . . . | 3 |  3 | 35 ♦  4 |  6 | 4
------------+---+----+----+----+----+--
x3o3o . . . ♦ 4 |  6 |  4 | 35 |  3 | 3
------------+---+----+----+----+----+--
x3o3o3o . . ♦ 5 | 10 | 10 |  5 | 21 | 2
------------+---+----+----+----+----+--
x3o3o3o3o . ♦ 6 | 15 | 20 | 15 |  6 | 7
x3o3o3o3o4o
. . . . . . | 12 ♦ 10 |  40 |  80 |  80 | 32
------------+----+----+-----+-----+-----+---
x . . . . . |  2 | 60 ♦   8 |  24 |  32 | 16
------------+----+----+-----+-----+-----+---
x3o . . . . |  3 |  3 | 160 ♦   6 |  12 |  8
------------+----+----+-----+-----+-----+---
x3o3o . . . ♦  4 |  6 |   4 | 240 |   4 |  4
------------+----+----+-----+-----+-----+---
x3o3o3o . . ♦  5 | 10 |  10 |   5 | 192 |  2
------------+----+----+-----+-----+-----+---
x3o3o3o3o . ♦  6 | 15 |  20 |  15 |   6 | 64
o3o3o3o3o4x
. . . . . . | 64 ♦   6 |  15 |  20 | 15 |  6
------------+----+-----+-----+-----+----+---
. . . . . x |  2 | 192 ♦   5 |  10 | 10 |  5
------------+----+-----+-----+-----+----+---
. . . . o4x |  4 |   4 | 240 ♦   4 |  6 |  4
------------+----+-----+-----+-----+----+---
. . . o3o4x ♦  8 |  12 |   6 | 160 |  3 |  3
------------+----+-----+-----+-----+----+---
. . o3o3o4x ♦ 16 |  32 |  24 |   8 | 60 |  2
------------+----+-----+-----+-----+----+---
. o3o3o3o4x ♦ 32 |  80 |  80 |  40 | 10 | 12

Uniform 6D[edit]

6D
6-demicube h{4,3,3,3,3} [57] 221 {3,3,32,1} [58] 122 {3,32,2} [59]
x3o3o *b3o3o3o
. . .    . . . | 32 ♦  15 |  60 |  20  60 | 15  30 |  6  6
---------------+----+-----+-----+---------+--------+------
x . .    . . . |  2 | 240 ♦   8 |   4  12 |  6   8 |  4  2
---------------+----+-----+-----+---------+--------+------
x3o .    . . . |  3 |   3 | 640 |   1   3 |  3   3 |  3  1
---------------+----+-----+-----+---------+--------+------
x3o3o    . . . ♦  4 |   6 |   4 | 160   * |  3   0 |  3  0
x3o . *b3o . . ♦  4 |   6 |   4 |   * 480 |  1   2 |  2  1
---------------+----+-----+-----+---------+--------+------
x3o3o *b3o . . ♦  8 |  24 |  32 |   8   8 | 60   * |  2  0
x3o . *b3o3o . ♦  5 |  10 |  10 |   0   5 |  * 192 |  1  1
---------------+----+-----+-----+---------+--------+------
x3o3o *b3o3o . ♦ 16 |  80 | 160 |  40  80 | 10  16 | 12  *
x3o . *b3o3o3o ♦  6 |  15 |  20 |   0  15 |  0   6 |  * 32
x3o3o3o3o *c3o
. . . . .    . | 27 ♦  16 |  80 |  160 |  80  40 | 16 10
---------------+----+-----+-----+------+---------+------
x . . . .    . |  2 | 216 ♦  10 |   30 |  20  10 |  5  5
---------------+----+-----+-----+------+---------+------
x3o . . .    . |  3 |   3 | 720 ♦    6 |   6   3 |  2  3
---------------+----+-----+-----+------+---------+------
x3o3o . .    . ♦  4 |   6 |   4 | 1080 |   2   1 |  1  2
---------------+----+-----+-----+------+---------+------
x3o3o3o .    . ♦  5 |  10 |  10 |    5 | 432   * |  1  1
x3o3o . . *c3o ♦  5 |  10 |  10 |    5 |   * 216 |  0  2
---------------+----+-----+-----+------+---------+------
x3o3o3o3o    . ♦  6 |  15 |  20 |   15 |   6   0 | 72  *
x3o3o3o . *c3o ♦ 10 |  40 |  80 |   80 |  16  16 |  * 27
o3o3o3o3o *c3x
. . . . .    . | 72 ♦  20 |   90 |   60   60 |  15  30  15 |  6  6
---------------+----+-----+------+-----------+-------------+------
. . . . .    x |  2 | 720 ♦    9 |    9    9 |   3   9   3 |  3  3
---------------+----+-----+------+-----------+-------------+------
. . o . . *c3x |  3 |   3 | 2160 |    2    2 |   1   4   1 |  2  2
---------------+----+-----+------+-----------+-------------+------
. o3o . . *c3x ♦  4 |   6 |    4 | 1080    * |   1   2   0 |  2  1
. . o3o . *c3x ♦  4 |   6 |    4 |    * 1080 |   0   2   1 |  1  2
---------------+----+-----+------+-----------+-------------+------
o3o3o . . *c3x ♦  5 |  10 |   10 |    5    0 | 216   *   * |  2  0
. o3o3o . *c3x ♦  8 |  24 |   32 |    8    8 |   * 270   * |  1  1
. . o3o3o *c3x ♦  5 |  10 |   10 |    0    5 |   *   * 216 |  0  2
---------------+----+-----+------+-----------+-------------+------
o3o3o3o . *c3x ♦ 16 |  80 |  160 |   80   40 |  16  10   0 | 27  *
. o3o3o3o *c3x ♦ 16 |  80 |  160 |   40   80 |   0  10  16 |  * 27
rectified 6-simplex
r{3,3,3,3,3} [60]
birectified 6-simplex
r{3,3,3,3,3} [61]
rectified 1_22
r{3,32,2} [62]
o3x3o3o3o3o - ril
. . . . . . | 21 ♦  10 |  5  20 | 10  20 | 10 10 | 5 2
------------+----+-----+--------+--------+-------+----
. x . . . . |  2 | 105 |  1   4 |  4   6 |  6  4 | 4 1
------------+----+-----+--------+--------+-------+----
o3x . . . . |  3 |   3 | 35   * ♦  4   0 |  6  0 | 4 0
. x3o . . . |  3 |   3 |  * 140 |  1   3 |  3  3 | 3 1
------------+----+-----+--------+--------+-------+----
o3x3o . . . ♦  6 |  12 |  4   4 | 35   * |  3  0 | 3 0
. x3o3o . . ♦  4 |   6 |  0   4 |  * 105 |  1  2 | 2 1
------------+----+-----+--------+--------+-------+----
o3x3o3o . . ♦ 10 |  30 | 10  20 |  5   5 | 21  * | 2 0
. x3o3o3o . ♦  5 |  10 |  0  10 |  0   5 |  * 42 | 1 1
------------+----+-----+--------+--------+-------+----
o3x3o3o3o . ♦ 15 |  60 | 20  60 | 15  30 |  6  6 | 7 *
. x3o3o3o3o ♦  6 |  15 |  0  20 |  0  15 |  0  6 | * 7
o3o3x3o3o3o - bril
. . . . . . | 35 ♦  12 |  12  18 |  4  18  12 |  6 12  3 | 4 3
------------+----+-----+---------+------------+----------+----
. . x . . . |  2 | 210 |   2   3 |  1   6   3 |  3  6  1 | 3 2
------------+----+-----+---------+------------+----------+----
. o3x . . . |  3 |   3 | 140   * |  1   3   0 |  3  3  0 | 3 1
. . x3o . . |  3 |   3 |   * 210 |  0   2   2 |  1  4  1 | 2 2
------------+----+-----+---------+------------+----------+----
o3o3x . . . ♦  4 |   6 |   4   0 | 35   *   * |  3  0  0 | 3 0
. o3x3o . . ♦  6 |  12 |   4   4 |  * 105   * |  1  2  0 | 2 1
. . x3o3o . ♦  4 |   6 |   0   4 |  *   * 105 |  0  2  1 | 1 2
------------+----+-----+---------+------------+----------+----
o3o3x3o . . ♦ 10 |  30 |  20  10 |  5   5   0 | 21  *  * | 2 0
. o3x3o3o . ♦ 10 |  30 |  10  20 |  0   5   5 |  * 42  * | 1 1
. . x3o3o3o ♦  5 |  10 |   0  10 |  0   0   5 |  *  * 21 | 0 2
------------+----+-----+---------+------------+----------+----
o3o3x3o3o . ♦ 20 |  90 |  60  60 | 15  30  15 |  6  6  0 | 7 *
. o3x3o3o3o ♦ 15 |  60 |  20  60 |  0  15  30 |  0  6  6 | * 7
o3o3x3o3o *c3o - ram
. . . . .    . | 720 ♦   18 |   18   18    9 |    6   18    9    6    9 |   6   3   6   9   3 |  2  3  3
---------------+-----+------+----------------+--------------------------+---------------------+---------
. . x . .    . |   2 | 6480 |    2    2    1 |    1    4    2    1    2 |   2   1   2   4   1 |  1  2  2
---------------+-----+------+----------------+--------------------------+---------------------+---------
. o3x . .    . |   3 |    3 | 4320    *    * |    1    2    1    0    0 |   2   1   1   2   0 |  1  2  1
. . x3o .    . |   3 |    3 |    * 4320    * |    0    2    0    1    1 |   1   0   2   2   1 |  1  1  2
. . x . . *c3o |   3 |    3 |    *    * 2160 |    0    0    2    0    2 |   0   1   0   4   1 |  0  2  2
---------------+-----+------+----------------+--------------------------+---------------------+---------
o3o3x . .    . ♦   4 |    6 |    4    0    0 | 1080    *    *    *    * |   2   1   0   0   0 |  1  2  0
. o3x3o .    . ♦   6 |   12 |    4    4    0 |    * 2160    *    *    * |   1   0   1   1   0 |  1  1  1
. o3x . . *c3o ♦   6 |   12 |    4    0    4 |    *    * 1080    *    * |   0   1   0   2   0 |  0  2  1
. . x3o3o    . ♦   4 |    6 |    0    4    0 |    *    *    * 1080    * |   0   0   2   0   1 |  1  0  2
. . x3o . *c3o ♦   6 |   12 |    0    4    4 |    *    *    *    * 1080 |   0   0   0   2   1 |  0  1  2
---------------+-----+------+----------------+--------------------------+---------------------+---------
o3o3x3o .    . ♦  10 |   30 |   20   10    0 |    5    5    0    0    0 | 432   *   *   *   * |  1  1  0
o3o3x . . *c3o ♦  10 |   30 |   20    0   10 |    5    0    5    0    0 |   * 216   *   *   * |  0  2  0
. o3x3o3o    . ♦  10 |   30 |   10   20    0 |    0    5    0    5    0 |   *   * 432   *   * |  1  0  1
. o3x3o . *c3o ♦  24 |   96 |   32   32   32 |    0    8    8    0    8 |   *   *   * 270   * |  0  1  1
. . x3o3o *c3o ♦  10 |   30 |    0   20   10 |    0    0    0    5    5 |   *   *   *   * 216 |  0  0  2
---------------+-----+------+----------------+--------------------------+---------------------+---------
o3o3x3o3o    . ♦  20 |   90 |   60   60    0 |   15   30    0   15    0 |   6   0   6   0   0 | 72  *  *
o3o3x3o . *c3o ♦  80 |  480 |  320  160  160 |   80   80   80    0   40 |  16  16   0  10   0 |  * 27  *
. o3x3o3o *c3o ♦  80 |  480 |  160  320  160 |    0   80   40   80   80 |   0   0  16  10  16 |  *  * 27

7D[edit]

7-simplex {3,3,3,3,3,3} [63] 7-orthoplex {3,3,3,3,3,4} [64] 7-cube {4,3,3,3,3,3} [65]
x3o3o3o3o3o3o
. . . . . . . | 8 ♦  7 | 21 | 35 | 35 | 21 | 7
--------------+---+----+----+----+----+----+--
x . . . . . . | 2 | 28 ♦  6 | 15 | 20 | 15 | 6
--------------+---+----+----+----+----+----+--
x3o . . . . . | 3 |  3 | 56 ♦  5 | 10 | 10 | 5
--------------+---+----+----+----+----+----+--
x3o3o . . . . ♦ 4 |  6 |  4 | 70 ♦  4 |  6 | 4
--------------+---+----+----+----+----+----+--
x3o3o3o . . . ♦ 5 | 10 | 10 |  5 | 56 |  3 | 3
--------------+---+----+----+----+----+----+--
x3o3o3o3o . . ♦ 6 | 15 | 20 | 15 |  6 | 28 | 2
--------------+---+----+----+----+----+----+--
x3o3o3o3o3o . ♦ 7 | 21 | 35 | 35 | 21 |  7 | 8
x3o3o3o3o3o4o
. . . . . . . | 14 ♦ 12 |  60 | 160 | 240 | 192 |  64
--------------+----+----+-----+-----+-----+-----+----
x . . . . . . |  2 | 84 ♦  10 |  40 |  80 |  80 |  32
--------------+----+----+-----+-----+-----+-----+----
x3o . . . . . |  3 |  3 | 280 ♦   8 |  24 |  32 |  16
--------------+----+----+-----+-----+-----+-----+----
x3o3o . . . . ♦  4 |  6 |   4 | 560 ♦   6 |  12 |   8
--------------+----+----+-----+-----+-----+-----+----
x3o3o3o . . . ♦  5 | 10 |  10 |   5 | 672 |   4 |   4
--------------+----+----+-----+-----+-----+-----+----
x3o3o3o3o . . ♦  6 | 15 |  20 |  15 |   6 | 448 |   2
--------------+----+----+-----+-----+-----+-----+----
x3o3o3o3o3o . ♦  7 | 21 |  35 |  35 |  21 |   7 | 128
o3o3o3o3o3o4x
. . . . . . . | 128 ♦   7 |  21 |  35 |  35 | 21 |  7
--------------+-----+-----+-----+-----+-----+----+---
. . . . . . x |   2 | 448 ♦   6 |  15 |  20 | 15 |  6
--------------+-----+-----+-----+-----+-----+----+---
. . . . . o4x |   4 |   4 | 672 ♦   5 |  10 | 10 |  5
--------------+-----+-----+-----+-----+-----+----+---
. . . . o3o4x ♦   8 |  12 |   6 | 560 ♦   4 |  6 |  4
--------------+-----+-----+-----+-----+-----+----+---
. . . o3o3o4x ♦  16 |  32 |  24 |   8 | 280 |  3 |  3
--------------+-----+-----+-----+-----+-----+----+---
. . o3o3o3o4x ♦  32 |  80 |  80 |  40 |  10 | 84 |  2
--------------+-----+-----+-----+-----+-----+----+---
. o3o3o3o3o4x ♦  64 | 192 | 240 | 160 |  60 | 12 | 14

Uniform 7D[edit]

7-demicube h{4,3,3,3,3,3} [66] 321 {3,3,3,32,1} [67]
x3o3o *b3o3o3o3o
. . .    . . . . | 64 ♦  21 |  105 |  35  140 |  35  105 | 21  42 |  7  7
-----------------+----+-----+------+----------+----------+--------+------
x . .    . . . . |  2 | 672 ♦   10 |   5   20 |  10   20 | 10  10 |  5  2
-----------------+----+-----+------+----------+----------+--------+------
x3o .    . . . . |  3 |   3 | 2240 |   1    4 |   4    6 |  6   4 |  4  1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o    . . . . ♦  4 |   6 |    4 | 560    * ♦   4    0 |  6   0 |  4  0
x3o . *b3o . . . ♦  4 |   6 |    4 |   * 2240 |   1    3 |  3   3 |  3  1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o *b3o . . . ♦  8 |  24 |   32 |   8    8 | 280    * |  3   0 |  3  0
x3o . *b3o3o . . ♦  5 |  10 |   10 |   0    5 |   * 1344 |  1   2 |  2  1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o *b3o3o . . ♦ 16 |  80 |  160 |  40   80 |  10   16 | 84   * |  2  0
x3o . *b3o3o3o . ♦  6 |  15 |   20 |   0   15 |   0    6 |  * 448 |  1  1
-----------------+----+-----+------+----------+----------+--------+------
x3o3o *b3o3o3o . ♦ 32 | 240 |  640 | 160  480 |  60  192 | 12  32 | 14  *
x3o . *b3o3o3o3o ♦  7 |  21 |   35 |   0   35 |   0   21 |  0   7 |  * 64
o3o3o3o *c3o3o3x
. . . .    . . . | 56 ♦  27 |  216 |   720 |  1080 |  432  216 |  72  27
-----------------+----+-----+------+-------+-------+-----------+--------
. . . .    . . x |  2 | 756 ♦   16 |    80 |   160 |   80   40 |  16  10
-----------------+----+-----+------+-------+-------+-----------+--------
. . . .    . o3x |  3 |   3 | 4032 ♦    10 |    30 |   20   10 |   5   5
-----------------+----+-----+------+-------+-------+-----------+--------
. . . .    o3o3x ♦  4 |   6 |    4 | 10080 ♦     6 |    6    3 |   2   3
-----------------+----+-----+------+-------+-------+-----------+--------
. . o . *c3o3o3x ♦  5 |  10 |   10 |     5 | 12096 |    2    1 |   1   2
-----------------+----+-----+------+-------+-------+-----------+--------
. o3o . *c3o3o3x ♦  6 |  15 |   20 |    15 |     6 | 4032    * |   1   1
. . o3o *c3o3o3x ♦  6 |  15 |   20 |    15 |     6 |    * 2016 |   0   2
-----------------+----+-----+------+-------+-------+-----------+--------
o3o3o . *c3o3o3x ♦  7 |  21 |   35 |    35 |    21 |   10    0 | 576   *
. o3o3o *c3o3o3x ♦ 12 |  60 |  160 |   240 |   192 |   32   32 |   * 126
231 {3,3,33,1} [68] 132 {3,33,2} [69]
x3o3o3o *c3o3o3o
. . . .    . . . | 126 ♦   32 |   240 |   640 |  160   480 |  60  192 | 12  32
-----------------+-----+------+-------+-------+------------+----------+-------
x . . .    . . . |   2 | 2016 ♦    15 |    60 |   20    60 |  15   30 |  6   6
-----------------+-----+------+-------+-------+------------+----------+-------
x3o . .    . . . |   3 |    3 | 10080 ♦     8 |    4    12 |   6    8 |  4   2
-----------------+-----+------+-------+-------+------------+----------+-------
x3o3o .    . . . ♦   4 |    6 |     4 | 20160 |    1     3 |   3    3 |  3   1
-----------------+-----+------+-------+-------+------------+----------+-------
x3o3o3o    . . . ♦   5 |   10 |    10 |     5 | 4032     * |   3    0 |  3   0
x3o3o . *c3o . . ♦   5 |   10 |    10 |     5 |    * 12096 |   1    2 |  2   1
-----------------+-----+------+-------+-------+------------+----------+-------
x3o3o3o *c3o . . ♦  10 |   40 |    80 |    80 |   16    16 | 756    * |  2   0
x3o3o . *c3o3o . ♦   6 |   15 |    20 |    15 |    0     6 |   * 4032 |  1   1
-----------------+-----+------+-------+-------+------------+----------+-------
x3o3o3o *c3o3o . ♦  27 |  216 |   720 |  1080 |  216   432 |  27   72 | 56   *
x3o3o . *c3o3o3o ♦   7 |   21 |    35 |    35 |    0    21 |   0    7 |  * 576
o3o3o3x *c3o3o3o
. . . .    . . . | 576 ♦    35 |   210 |   140   210 |   35  105   105 |  21   42   21 |  7   7
-----------------+-----+-------+-------+-------------+-----------------+---------------+-------
. . . x    . . . |   2 | 10080 ♦    12 |    12    18 |    4   12    12 |   6   12    3 |  4   3
-----------------+-----+-------+-------+-------------+-----------------+---------------+-------
. . o3x    . . . |   3 |     3 | 40320 |     2     3 |    1    6     3 |   3    6    1 |  3   2
-----------------+-----+-------+-------+-------------+-----------------+---------------+-------
. o3o3x    . . . ♦   4 |     6 |     4 | 20160     * |    1    3     0 |   3    3    0 |  3   1
. . o3x *c3o . . ♦   4 |     6 |     4 |     * 30240 |    0    2     2 |   1    4    1 |  2   2
-----------------+-----+-------+-------+-------------+-----------------+---------------+-------
o3o3o3x    . . . ♦   5 |    10 |    10 |     5     0 | 4032    *     * |   3    0    0 |  3   0
. o3o3x *c3o . . ♦   8 |    24 |    32 |     8     8 |    * 7560     * |   1    2    0 |  2   1
. . o3x *c3o3o . ♦   5 |    10 |    10 |     0     5 |    *    * 12096 |   0    2    1 |  1   2
-----------------+-----+-------+-------+-------------+-----------------+---------------+-------
o3o3o3x *c3o . . ♦  16 |    80 |   160 |    80    40 |   16   10     0 | 756    *    * |  2   0
. o3o3x *c3o3o . ♦  16 |    80 |   160 |    40    80 |    0   10    16 |   * 1512    * |  1   1
. . o3x *c3o3o3o ♦   6 |    15 |    20 |     0    15 |    0    0     6 |   *    * 2016 |  0   2
-----------------+-----+-------+-------+-------------+-----------------+---------------+-------
o3o3o3x *c3o3o . ♦  72 |   720 |  2160 |  1080  1080 |  216  270   216 |  27   27    0 | 56   *
. o3o3x *c3o3o3o ♦  32 |   240 |   640 |   160   480 |    0   60   192 |   0   12   32 |  * 126
051 r{3,3,3,3,3,3} [70] 042 2r{3,3,3,3,3,3} [71]
o3x3o3o3o3o3o - roc
. . . . . . . | 28 ♦  12 |  6  30 | 15  40 | 20  30 | 15 12 | 6 2
--------------+----+-----+--------+--------+--------+-------+----
. x . . . . . |  2 | 168 |  1   5 |  5  10 | 10  10 | 10  5 | 5 1
--------------+----+-----+--------+--------+--------+-------+----
o3x . . . . . |  3 |   3 | 56   * ♦  5   0 | 10   0 | 10  0 | 5 0
. x3o . . . . |  3 |   3 |  * 280 |  1   4 |  4   6 |  6  4 | 4 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o . . . . ♦  6 |  12 |  4   4 | 70   * ♦  4   0 |  6  0 | 4 0
. x3o3o . . . ♦  4 |   6 |  0   4 |  * 280 |  1   3 |  3  3 | 3 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o3o . . . ♦ 10 |  30 | 10  20 |  5   5 | 56   * |  3  0 | 3 0
. x3o3o3o . . ♦  5 |  10 |  0  10 |  0   5 |  * 168 |  1  2 | 2 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o3o3o . . ♦ 15 |  60 | 20  60 | 15  30 |  6   6 | 28  * | 2 0
. x3o3o3o3o . ♦  6 |  15 |  0  20 |  0  15 |  0   6 |  * 56 | 1 1
--------------+----+-----+--------+--------+--------+-------+----
o3x3o3o3o3o . ♦ 21 | 105 | 35 140 | 35 105 | 21  42 |  7  7 | 8 *
. x3o3o3o3o3o ♦  7 |  21 |  0  35 |  0  35 |  0  21 |  0  7 | * 8
o3o3x3o3o3o3o - broc
. . . . . . . | 56 ♦  15 |  15  30 |  5  30  30 | 10  30  15 | 10 15  3 | 5 3
--------------+----+-----+---------+------------+------------+----------+----
. . x . . . . |  2 | 420 |   2   4 |  1   8   6 |  4  12   4 |  6  8  1 | 4 2
--------------+----+-----+---------+------------+------------+----------+----
. o3x . . . . |  3 |   3 | 280   * |  1   4   0 |  4   6   0 |  6  4  0 | 4 1
. . x3o . . . |  3 |   3 |   * 560 |  0   2   3 |  1   6   3 |  3  6  1 | 3 2
--------------+----+-----+---------+------------+------------+----------+----
o3o3x . . . . ♦  4 |   6 |   4   0 | 70   *   * ♦  4   0   0 |  6  0  0 | 4 0
. o3x3o . . . ♦  6 |  12 |   4   4 |  * 280   * |  1   3   0 |  3  3  0 | 3 1
. . x3o3o . . ♦  4 |   6 |   0   4 |  *   * 420 |  0   2   2 |  1  4  1 | 2 2
--------------+----+-----+---------+------------+------------+----------+----
o3o3x3o . . . ♦ 10 |  30 |  20  10 |  5   5   0 | 56   *   * |  3  0  0 | 3 0
. o3x3o3o . . ♦ 10 |  30 |  10  20 |  0   5   5 |  * 168   * |  1  2  0 | 2 1
. . x3o3o3o . ♦  5 |  10 |   0  10 |  0   0   5 |  *   * 168 |  0  2  1 | 1 2
--------------+----+-----+---------+------------+------------+----------+----
o3o3x3o3o . . ♦ 20 |  90 |  60  60 | 15  30  15 |  6   6   0 | 28  *  * | 2 0
. o3x3o3o3o . ♦ 15 |  60 |  20  60 |  0  15  30 |  0   6   6 |  * 56  * | 1 1
. . x3o3o3o3o ♦  6 |  15 |   0  20 |  0   0  15 |  0   0   6 |  *  * 28 | 0 2
--------------+----+-----+---------+------------+------------+----------+----
o3o3x3o3o3o . ♦ 35 | 210 | 140 210 | 35 105 105 | 21  42  21 |  7  7  0 | 8 *
. o3x3o3o3o3o ♦ 21 | 105 |  35 140 |  0  35 105 |  0  21  42 |  0  7  7 | * 8
033 3r{3,3,3,3,3,3} [72]
o3o3o3x3o3o3o - he
. . . . . . . | 70 ♦  16 |  24  24 |  16  36  16 |  4  24  24  4 |  6 16  6 | 4 4
--------------+----+-----+---------+-------------+---------------+----------+----
. . . x . . . |  2 | 560 |   3   3 |   3   9   3 |  1   9   9  1 |  3  9  3 | 3 3
--------------+----+-----+---------+-------------+---------------+----------+----
. . o3x . . . |  3 |   3 | 560   * |   2   3   0 |  1   6   3  0 |  3  6  1 | 3 2
. . . x3o . . |  3 |   3 |   * 560 |   0   3   2 |  0   3   6  1 |  1  6  3 | 2 3
--------------+----+-----+---------+-------------+---------------+----------+----
. o3o3x . . . ♦  4 |   6 |   4   0 | 280   *   * |  1   3   0  0 |  3  3  0 | 3 1
. . o3x3o . . ♦  6 |  12 |   4   4 |   * 420   * |  0   2   2  0 |  1  4  1 | 2 2
. . . x3o3o . ♦  4 |   6 |   0   4 |   *   * 280 |  0   0   3  1 |  0  3  3 | 1 3
--------------+----+-----+---------+-------------+---------------+----------+----
o3o3o3x . . . ♦  5 |  10 |  10   0 |   5   0   0 | 56   *   *  * |  3  0  0 | 3 0
. o3o3x3o . . ♦ 10 |  30 |  20  10 |   5   5   0 |  * 168   *  * |  1  2  0 | 2 1
. . o3x3o3o . ♦ 10 |  30 |  10  20 |   0   5   5 |  *   * 168  * |  0  2  1 | 1 2
. . . x3o3o3o ♦  5 |  10 |   0  10 |   0   0   5 |  *   *   * 56 |  0  0  3 | 0 3
--------------+----+-----+---------+-------------+---------------+----------+----
o3o3o3x3o . . ♦ 15 |  60 |  60  20 |  30  15   0 |  6   6   0  0 | 28  *  * | 2 0
. o3o3x3o3o . ♦ 20 |  90 |  60  60 |  15  30  15 |  0   6   6  0 |  * 56  * | 1 1
. . o3x3o3o3o ♦ 15 |  60 |  20  60 |   0  15  30 |  0   0   6  6 |  *  * 28 | 0 2
--------------+----+-----+---------+-------------+---------------+----------+----
o3o3o3x3o3o . ♦ 35 | 210 | 210 140 | 105 105  35 | 21  42  21  0 |  7  7  0 | 8 *
. o3o3x3o3o3o ♦ 35 | 210 | 140 210 |  35 105 105 |  0  21  42 21 |  0  7  7 | * 8
0321 r{3,33,2} [73]
o3o3x3o *c3o3o3o - rolin

. . . .    . . . | 10080 ♦     24 |    24    12     36 |     8    12    36    18    24 |    4    12   18    24    12     6 |   6    8   12    6    3 |  4   2   3
-----------------+-------+--------+--------------------+-------------------------------+-----------------------------------+-------------------------+-----------
. . x .    . . . |     2 | 120960 |     2     1      3 |     1     2     6     3     3 |    1     3    6     6     3     1 |   3    3    6    2    1 |  3   1   2
-----------------+-------+--------+--------------------+-------------------------------+-----------------------------------+-------------------------+-----------
. o3x .    . . . |     3 |      3 | 80640     *      * |     1     1     3     0     0 |    1     3    3     3     0     0 |   3    3    3    1    0 |  3   1   1
. . x3o    . . . |     3 |      3 |     * 40320      * |     0     2     0     3     0 |    1     0    6     0     3     0 |   3    0    6    0    1 |  3   0   2
. . x . *c3o . . |     3 |      3 |     *     * 120960 |     0     0     2     1     2 |    0     1    2     4     2     1 |   1    2    4    2    1 |  2   1   2
-----------------+-------+--------+--------------------+-------------------------------+-----------------------------------+-------------------------+-----------
o3o3x .    . . . ♦     4 |      6 |     4     0      0 | 20160     *     *     *     * |    1     3    0     0     0     0 |   3    3    0    0    0 |  3   1   0
. o3x3o    . . . ♦     6 |     12 |     4     4      0 |     * 20160     *     *     * |    1     0    3     0     0     0 |   3    0    3    0    0 |  3   0   1
. o3x . *c3o . . ♦     6 |     12 |     4     0      4 |     *     * 60480     *     * |    0     1    1     2     0     0 |   1    2    2    1    0 |  2   1   1
. . x3o *c3o . . ♦     6 |     12 |     0     4      4 |     *     *     * 30240     * |    0     0    2     0     2     0 |   1    0    4    0    1 |  2   0   2
. . x . *c3o3o . ♦     4 |      6 |     0     0      4 |     *     *     *     * 60480 |    0     0    0     2     1     1 |   0    1    2    2    1 |  1   1   2
-----------------+-------+--------+--------------------+-------------------------------+-----------------------------------+-------------------------+-----------
o3o3x3o    . . . ♦    10 |     30 |    20    10      0 |     5     5     0     0     0 | 4032     *    *     *     *     * |   3    0    0    0    0 |  3   0   0
o3o3x . *c3o . . ♦    10 |     30 |    20     0     10 |     5     0     5     0     0 |    * 12096    *     *     *     * |   1    2    0    0    0 |  2   1   0
. o3x3o *c3o . . ♦    24 |     96 |    32    32     32 |     0     8     8     8     0 |    *     * 7560     *     *     * |   1    0    2    0    0 |  2   0   1
. o3x . *c3o3o . ♦    10 |     30 |    10     0     20 |     0     0     5     0     5 |    *     *    * 24192     *     * |   0    1    1    1    0 |  1   1   1
. . x3o *c3o3o . ♦    10 |     30 |     0    10     20 |     0     0     0     5     5 |    *     *    *     * 12096     * |   0    0    2    0    1 |  1   0   2
. . x . *c3o3o3o ♦     5 |     10 |     0     0     10 |     0     0     0     0     5 |    *     *    *     *     * 12096 |   0    0    0    2    1 |  0   1   2
-----------------+-------+--------+--------------------+-------------------------------+-----------------------------------+-------------------------+-----------
o3o3x3o *c3o . . ♦    80 |    480 |   320   160    160 |    80    80    80    40     0 |   16    16   10     0     0     0 | 756    *    *    *    * |  2   0   0
o3o3x . *c3o3o . ♦    20 |     90 |    60     0     60 |    15     0    30     0    15 |    0     6    0     6     0     0 |   * 4032    *    *    * |  1   1   0
. o3x3o *c3o3o . ♦    80 |    480 |   160   160    320 |     0    40    80    80    80 |    0     0   10    16    16     0 |   *    * 1512    *    * |  1   0   1
. o3x . *c3o3o3o ♦    15 |     60 |    20     0     60 |     0     0    15     0    30 |    0     0    0     6     0     6 |   *    *    * 4032    * |  0   1   1
. . x3o *c3o3o3o ♦    15 |     60 |     0    20     60 |     0     0     0    15    30 |    0     0    0     0     6     6 |   *    *    *    * 2016 |  0   0   2
-----------------+-------+--------+--------------------+-------------------------------+-----------------------------------+-------------------------+-----------
o3o3x3o *c3o3o . ♦   720 |   6480 |  4320  2160   4320 |  1080  1080  2160  1080  1080 |  216   432  270   432   216     0 |  27   72   27    0    0 | 56   *   *
o3o3x . *c3o3o3o ♦    35 |    210 |   140     0    210 |    35     0   105     0   105 |    0    21    0    42     0    21 |   0    7    0    7    0 |  * 576   *
. o3x3o *c3o3o3o ♦   240 |   1920 |   640   640   1920 |     0   160   480   480   960 |    0     0   60   192   192   192 |   0    0   12   32   32 |  *   * 126

8D[edit]

8D regular
8-simplex {3,3,3,3,3,3,3} [74] 8-orthoplex {3,3,3,3,3,3,4} [75] 8-cube {4,3,3,3,3,3,3} [76]
x3o3o3o3o3o3o3o
. . . . . . . . | 9 ♦  8 | 28 |  56 |  70 | 56 | 28 | 8
----------------+---+----+----+-----+-----+----+----+--
x . . . . . . . | 2 | 36 ♦  7 |  21 |  35 | 35 | 21 | 7
----------------+---+----+----+-----+-----+----+----+--
x3o . . . . . . | 3 |  3 | 84 ♦   6 |  15 | 20 | 15 | 6
----------------+---+----+----+-----+-----+----+----+--
x3o3o . . . . . ♦ 4 |  6 |  4 | 126 ♦   5 | 10 | 10 | 5
----------------+---+----+----+-----+-----+----+----+--
x3o3o3o . . . . ♦ 5 | 10 | 10 |   5 | 126 ♦  4 |  6 | 4
----------------+---+----+----+-----+-----+----+----+--
x3o3o3o3o . . . ♦ 6 | 15 | 20 |  15 |   6 | 84 |  3 | 3
----------------+---+----+----+-----+-----+----+----+--
x3o3o3o3o3o . . ♦ 7 | 21 | 35 |  35 |  21 |  7 | 36 | 2
----------------+---+----+----+-----+-----+----+----+--
x3o3o3o3o3o3o . ♦ 8 | 28 | 56 |  70 |  56 | 28 |  8 | 9
x3o3o3o3o3o3o4o
. . . . . . . . | 16 ♦  14 |  84 |  280 |  560 |  672 |  448 | 128
----------------+----+-----+-----+------+------+------+------+----
x . . . . . . . |  2 | 112 ♦  12 |   60 |  160 |  240 |  192 |  64
----------------+----+-----+-----+------+------+------+------+----
x3o . . . . . . |  3 |   3 | 448 ♦   10 |   40 |   80 |   80 |  32
----------------+----+-----+-----+------+------+------+------+----
x3o3o . . . . . ♦  4 |   6 |   4 | 1120 ♦    8 |   24 |   32 |  16
----------------+----+-----+-----+------+------+------+------+----
x3o3o3o . . . . ♦  5 |  10 |  10 |    5 | 1792 ♦    6 |   12 |   8
----------------+----+-----+-----+------+------+------+------+----
x3o3o3o3o . . . ♦  6 |  15 |  20 |   15 |    6 | 1792 |    4 |   4
----------------+----+-----+-----+------+------+------+------+----
x3o3o3o3o3o . . ♦  7 |  21 |  35 |   35 |   21 |    7 | 1024 |   2
----------------+----+-----+-----+------+------+------+------+----
x3o3o3o3o3o3o . ♦  8 |  28 |  56 |   70 |   56 |   28 |    8 | 256
o3o3o3o3o3o3o4x
. . . . . . . . | 256 ♦    8 |   28 |   56 |   70 |  56 |  28 |  8
----------------+-----+------+------+------+------+-----+-----+---
. . . . . . . x |   2 | 1024 ♦    7 |   21 |   35 |  35 |  21 |  7
----------------+-----+------+------+------+------+-----+-----+---
. . . . . . o4x |   4 |    4 | 1792 ♦    6 |   15 |  20 |  15 |  6
----------------+-----+------+------+------+------+-----+-----+---
. . . . . o3o4x ♦   8 |   12 |    6 | 1792 ♦    5 |  10 |  10 |  5
----------------+-----+------+------+------+------+-----+-----+---
. . . . o3o3o4x ♦  16 |   32 |   24 |    8 | 1120 ♦   4 |   6 |  4
----------------+-----+------+------+------+------+-----+-----+---
. . . o3o3o3o4x ♦  32 |   80 |   80 |   40 |   10 | 448 |   3 |  3
----------------+-----+------+------+------+------+-----+-----+---
. . o3o3o3o3o4x ♦  64 |  192 |  240 |  160 |   60 |  12 | 112 |  2
----------------+-----+------+------+------+------+-----+-----+---
. o3o3o3o3o3o4x ♦ 128 |  448 |  672 |  560 |  280 |  84 |  14 | 16

Uniform 8D[edit]

8-demicube h{4,3,3,3,3,3,3} [77] 421 {3,3,3,3,32,1} [78]
x3o3o *b3o3o3o3o3o
. . .    . . . . . | 128 ♦   28 |  168 |   56  280 |   70  280 |  56  168 |  28   56 |  8   8
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x . .    . . . . . |   2 | 1792 ♦   12 |    6   30 |   15   40 |  20   30 |  15   12 |  6   2
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o .    . . . . . |   3 |    3 | 7168 |    1    5 |    5   10 |  10   10 |  10    5 |  5   1
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o3o    . . . . . ♦   4 |    6 |    4 | 1792    * ♦    5    0 |  10    0 |  10    0 |  5   0
x3o . *b3o . . . . ♦   4 |    6 |    4 |    * 8960 |    1    4 |   4    6 |   6    4 |  4   1
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o3o *b3o . . . . ♦   8 |   24 |   32 |    8    8 | 1120    * ♦   4    0 |   6    0 |  4   0
x3o . *b3o3o . . . ♦   5 |   10 |   10 |    0    5 |    * 7168 |   1    3 |   3    3 |  3   1
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o3o *b3o3o . . . ♦  16 |   80 |  160 |   40   80 |   10   16 | 448    * |   3    0 |  3   0
x3o . *b3o3o3o . . ♦   6 |   15 |   20 |    0   15 |    0    6 |   * 3584 |   1    2 |  2   1
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o3o *b3o3o3o . . ♦  32 |  240 |  640 |  160  480 |   60  192 |  12   32 | 112    * |  2   0
x3o . *b3o3o3o3o . ♦   7 |   21 |   35 |    0   35 |    0   21 |   0    7 |   * 1024 |  1   1
-------------------+-----+------+------+-----------+-----------+----------+----------+-------
x3o3o *b3o3o3o3o . ♦  64 |  672 | 2240 |  560 2240 |  280 1344 |  84  448 |  14   64 | 16   *
x3o . *b3o3o3o3o3o ♦   8 |   28 |   56 |    0   70 |    0   56 |   0   28 |   0    8 |  * 128

o3o3o3o *c3o3o3o3x
. . . .    . . . . | 240 ♦   56 |   756 |   4032 |  10080 |  12096 |   4032  2016 |   576  126
-------------------+-----+------+-------+--------+--------+--------+--------------+-----------
. . . .    . . . x |   2 | 6720 ♦    27 |    216 |    720 |   1080 |    432   216 |    72   27
-------------------+-----+------+-------+--------+--------+--------+--------------+-----------
. . . .    . . o3x |   3 |    3 | 60480 ♦     16 |     80 |    160 |     80    40 |    16   10
-------------------+-----+------+-------+--------+--------+--------+--------------+-----------
. . . .    . o3o3x ♦   4 |    6 |     4 | 241920 ♦     10 |     30 |     20    10 |     5    5
-------------------+-----+------+-------+--------+--------+--------+--------------+-----------
. . . .    o3o3o3x ♦   5 |   10 |    10 |      5 | 483840 ♦      6 |      6     3 |     2    3
-------------------+-----+------+-------+--------+--------+--------+--------------+-----------
. . o . *c3o3o3o3x ♦   6 |   15 |    20 |     15 |      6 | 483840 |      2     1 |     1    2
-------------------+-----+------+-------+--------+--------+--------+--------------+-----------
. o3o . *c3o3o3o3x ♦   7 |   21 |    35 |     35 |     21 |      7 | 138240     * |     1    1
. . o3o *c3o3o3o3x ♦   7 |   21 |    35 |     35 |     21 |      7 |      * 69120 |     0    2
-------------------+-----+------+-------+--------+--------+--------+--------------+-----------
o3o3o . *c3o3o3o3x ♦   8 |   28 |    56 |     70 |     56 |     28 |      8     0 | 17280    *
. o3o3o *c3o3o3o3x ♦  14 |   84 |   280 |    560 |    672 |    448 |     64    64 |     * 2160
241 {3,3,34,1} [79] 142 {3,34,2} [80]

x3o3o3o *c3o3o3o3o
. . . .    . . . . | 2160 ♦    64 |    672 |    2240 |    560   2240 |   280   1344 |   84    448 |  14   64
-------------------+------+-------+--------+---------+---------------+--------------+-------------+---------
x . . .    . . . . |    2 | 69120 ♦     21 |     105 |     35    140 |    35    105 |   21     42 |   7    7
-------------------+------+-------+--------+---------+---------------+--------------+-------------+---------
x3o . .    . . . . |    3 |     3 | 483840 ♦      10 |      5     20 |    10     20 |   10     10 |   5    2
-------------------+------+-------+--------+---------+---------------+--------------+-------------+---------
x3o3o .    . . . . ♦    4 |     6 |      4 | 1209600 |      1      4 |     4      6 |    6      4 |   4    1
-------------------+------+-------+--------+---------+---------------+--------------+-------------+---------
x3o3o3o    . . . . ♦    5 |    10 |     10 |       5 | 241920      * |     4      0 |    6      0 |   4    0
x3o3o . *c3o . . . ♦    5 |    10 |     10 |       5 |      * 967680 |     1      3 |    3      3 |   3    1
-------------------+------+-------+--------+---------+---------------+--------------+-------------+---------
x3o3o3o *c3o . . . ♦   10 |    40 |     80 |      80 |     16     16 | 60480      * |    3      0 |   3    0
x3o3o . *c3o3o . . ♦    6 |    15 |     20 |      15 |      0      6 |     * 483840 |    1      2 |   2    1
-------------------+------+-------+--------+---------+---------------+--------------+-------------+---------
x3o3o3o *c3o3o . . ♦   27 |   216 |    720 |    1080 |    216    432 |    27     72 | 6720      * |   2    0
x3o3o . *c3o3o3o . ♦    7 |    21 |     35 |      35 |      0     21 |     0      7 |    * 138240 |   1    1
-------------------+------+-------+--------+---------+---------------+--------------+-------------+---------
x3o3o3o *c3o3o3o . ♦  126 |  2016 |  10080 |   20160 |   4032  12096 |   756   4032 |   56    576 | 240    *
x3o3o . *c3o3o3o3o ♦    8 |    28 |     56 |      70 |      0     56 |     0     28 |    0      8 |  * 17280
o3o3o3x *c3o3o3o3o
. . . .    . . . . | 17280 ♦     56 |     420 |     280     560 |     70    280      420 |    56    168    168 |   28    56    28 |   8    8
-------------------+-------+--------+---------+-----------------+------------------------+---------------------+------------------+---------
. . . x    . . . . |     2 | 483840 ♦      15 |      15      30 |      5     30       30 |    10     30     15 |   10    15     3 |   5    3
-------------------+-------+--------+---------+-----------------+------------------------+---------------------+------------------+---------
. . o3x    . . . . |     3 |      3 | 2419200 |       2       4 |      1      8        6 |     4     12      4 |    6     8     1 |   4    2
-------------------+-------+--------+---------+-----------------+------------------------+---------------------+------------------+---------
. o3o3x    . . . . ♦     4 |      6 |       4 | 1209600       * |      1      4        0 |     4      6      0 |    6     4     0 |   4    1
. . o3x *c3o . . . ♦     4 |      6 |       4 |       * 2419200 |      0      2        3 |     1      6      3 |    3     6     1 |   3    2
-------------------+-------+--------+---------+-----------------+------------------------+---------------------+------------------+---------
o3o3o3x    . . . . ♦     5 |     10 |      10 |       5       0 | 241920      *        * |     4      0      0 |    6     0     0 |   4    0
. o3o3x *c3o . . . ♦     8 |     24 |      32 |       8       8 |      * 604800        * |     1      3      0 |    3     3     0 |   3    1
. . o3x *c3o3o . . ♦     5 |     10 |      10 |       0       5 |      *      *  1451520 |     0      2      2 |    1     4     1 |   2    2
-------------------+-------+--------+---------+-----------------+------------------------+---------------------+------------------+---------
o3o3o3x *c3o . . . ♦    16 |     80 |     160 |      80      40 |     16     10        0 | 60480      *      * |    3     0     0 |   3    0
. o3o3x *c3o3o . . ♦    16 |     80 |     160 |      40      80 |      0     10       16 |     * 181440      * |    1     2     0 |   2    1
. . o3x *c3o3o3o . ♦     6 |     15 |      20 |       0      15 |      0      0        6 |     *      * 483840 |    0     2     1 |   1    2
-------------------+-------+--------+---------+-----------------+------------------------+---------------------+------------------+---------
o3o3o3x *c3o3o . . ♦    72 |    720 |    2160 |    1080    1080 |    216    270      216 |    27     27      0 | 6720     *     * |   2    0
. o3o3x *c3o3o3o . ♦    32 |    240 |     640 |     160     480 |      0     60      192 |     0     12     32 |    * 30240     * |   1    1
. . o3x *c3o3o3o3o ♦     7 |     21 |      35 |       0      35 |      0      0       21 |     0      0      7 |    *     * 69120 |   0    2
-------------------+-------+--------+---------+-----------------+------------------------+---------------------+------------------+---------
o3o3o3x *c3o3o3o . ♦   576 |  10080 |   40320 |   20160   30240 |   4032   7560    12096 |   756   1512   2016 |   56   126     0 | 240    *
. o3o3x *c3o3o3o3o ♦    64 |    672 |    2240 |     560    2240 |      0    280     1344 |     0     84    448 |    0    14    64 |   * 2160
061 r{3,3,3,3,3,3,3} [81] 052 2r{3,3,3,3,3,3,3} [82]
o3x3o3o3o3o3o3o - rene
. . . . . . . . | 36 ♦  14 |  7  42 |  21  70 |  35  70 | 35  42 | 21 14 | 7 2
----------------+----+-----+--------+---------+---------+--------+-------+----
. x . . . . . . |  2 | 252 |  1   6 |   6  15 |  15  20 | 20  15 | 15  6 | 6 1
----------------+----+-----+--------+---------+---------+--------+-------+----
o3x . . . . . . |  3 |   3 | 84   * ♦   6   0 |  15   0 | 20   0 | 15  0 | 6 0
. x3o . . . . . |  3 |   3 |  * 504 |   1   5 |   5  10 | 10  10 | 10  5 | 5 1
----------------+----+-----+--------+---------+---------+--------+-------+----
o3x3o . . . . . ♦  6 |  12 |  4   4 | 126   * ♦   5   0 | 10   0 | 10  0 | 5 0
. x3o3o . . . . ♦  4 |   6 |  0   4 |   * 630 |   1   4 |  4   6 |  6  4 | 4 1
----------------+----+-----+--------+---------+---------+--------+-------+----
o3x3o3o . . . . ♦ 10 |  30 | 10  20 |   5   5 | 126   * ♦  4   0 |  6  0 | 4 0
. x3o3o3o . . . ♦  5 |  10 |  0  10 |   0   5 |   * 504 |  1   3 |  3  3 | 3 1
----------------+----+-----+--------+---------+---------+--------+-------+----
o3x3o3o3o . . . ♦ 15 |  60 | 20  60 |  15  30 |   6   6 | 84   * |  3  0 | 3 0
. x3o3o3o3o . . ♦  6 |  15 |  0  20 |   0  15 |   0   6 |  * 252 |  1  2 | 2 1
----------------+----+-----+--------+---------+---------+--------+-------+----
o3x3o3o3o3o . . ♦ 21 | 105 | 35 140 |  35 105 |  21  42 |  7   7 | 36  * | 2 0
. x3o3o3o3o3o . ♦  7 |  21 |  0  35 |   0  35 |   0  21 |  0   7 |  * 72 | 1 1
----------------+----+-----+--------+---------+---------+--------+-------+----
o3x3o3o3o3o3o . ♦ 28 | 168 | 56 280 |  70 280 |  56 168 | 28  56 |  8  8 | 9 *
. x3o3o3o3o3o3o ♦  8 |  28 |  0  56 |   0  70 |   0  56 |  0  28 |  0  8 | * 9
o3o3x3o3o3o3o3o - brene
. . . . . . . . | 84 ♦  18 |  18   45 |   6  45   60 |  15  60  45 | 20  45  18 | 15 18  3 | 6 3
----------------+----+-----+----------+--------------+-------------+------------+----------+----
. . x . . . . . |  2 | 756 |   2    5 |   1  10   10 |   5  20  10 | 10  20   5 | 10 10  1 | 5 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
. o3x . . . . . |  3 |   3 | 504    * |   1   5    0 |   5  10   0 | 10  10   0 | 10  5  0 | 5 1
. . x3o . . . . |  3 |   3 |   * 1260 |   0   2    4 |   1   8   6 |  6  12   4 |  6  8  1 | 4 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
o3o3x . . . . . ♦  4 |   6 |   4    0 | 126   *    * ♦   5   0   0 | 10   0   0 | 10  0  0 | 5 0
. o3x3o . . . . ♦  6 |  12 |   4    4 |   * 630    * |   1   4   0 |  4   6   0 |  6  4  0 | 4 1
. . x3o3o . . . ♦  4 |   6 |   0    4 |   *   * 1260 |   0   2   3 |  1   6   3 |  3  6  1 | 3 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
o3o3x3o . . . . ♦ 10 |  30 |  20   10 |   5   5    0 | 126   *   * ♦  4   0   0 |  6  0  0 | 4 0
. o3x3o3o . . . ♦ 10 |  30 |  10   20 |   0   5    5 |   * 504   * |  1   3   0 |  3  3  0 | 3 1
. . x3o3o3o . . ♦  5 |  10 |   0   10 |   0   0    5 |   *   * 756 |  0   2   2 |  1  4  1 | 2 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
o3o3x3o3o . . . ♦ 20 |  90 |  60   60 |  15  30   15 |   6   6   0 | 84   *   * |  3  0  0 | 3 0
. o3x3o3o3o . . ♦ 15 |  60 |  20   60 |   0  15   30 |   0   6   6 |  * 252   * |  1  2  0 | 2 1
. . x3o3o3o3o . ♦  6 |  15 |   0   20 |   0   0   15 |   0   0   6 |  *   * 252 |  0  2  1 | 1 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
o3o3x3o3o3o . . ♦ 35 | 210 | 140  210 |  35 105  105 |  21  42  21 |  7   7   0 | 36  *  * | 2 0
. o3x3o3o3o3o . ♦ 21 | 105 |  35  140 |   0  35  105 |   0  21  42 |  0   7   7 |  * 72  * | 1 1
. . x3o3o3o3o3o ♦  7 |  21 |   0   35 |   0   0   35 |   0   0  21 |  0   0   7 |  *  * 36 | 0 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
o3o3x3o3o3o3o . ♦ 56 | 420 | 280  560 |  70 280  420 |  56 168 168 | 28  56  28 |  8  8  0 | 9 *
. o3x3o3o3o3o3o ♦ 28 | 168 |  56  280 |   0  70  280 |   0  56 168 |  0  28  56 |  0  8  8 | * 9
043 3r{3,3,3,3,3,3,3} [83]
o3o3o3x3o3o3o3o - trene
. . . . . . . . | 126 ♦   20 |   30   40 |  20   60   40 |   5  40  60  20 | 10  40  30  4 | 10 20  6 | 5 4
----------------+-----+------+-----------+---------------+-----------------+---------------+----------+----
. . . x . . . . |   2 | 1260 |    3    4 |   3   12    6 |   1  12  18   4 |  4  18  12  1 |  6 12  3 | 4 3
----------------+-----+------+-----------+---------------+-----------------+---------------+----------+----
. . o3x . . . . |   3 |    3 | 1260    * |   2    4    0 |   1   8   6   0 |  4  12   4  0 |  6  8  1 | 4 2
. . . x3o . . . |   3 |    3 |    * 1680 |   0    3    3 |   0   3   9   3 |  1   9   9  1 |  3  9  3 | 3 3
----------------+-----+------+-----------+---------------+-----------------+---------------+----------+----
. o3o3x . . . . ♦   4 |    6 |    4    0 | 630    *    * |   1   4   0   0 |  4   6   0  0 |  6  4  0 | 4 1
. . o3x3o . . . ♦   6 |   12 |    4    4 |   * 1260    * |   0   2   3   0 |  1   6   3  0 |  3  6  1 | 3 2
. . . x3o3o . . ♦   4 |    6 |    0    4 |   *    * 1260 |   0   0   3   2 |  0   3   6  1 |  1  6  3 | 2 3
----------------+-----+------+-----------+---------------+-----------------+---------------+----------+----
o3o3o3x . . . . ♦   5 |   10 |   10    0 |   5    0    0 | 126   *   *   * ♦  4   0   0  0 |  6  0  0 | 4 0
. o3o3x3o . . . ♦  10 |   30 |   20   10 |   5    5    0 |   * 504   *   * |  1   3   0  0 |  3  3  0 | 3 1
. . o3x3o3o . . ♦  10 |   30 |   10   20 |   0    5    5 |   *   * 756   * |  0   2   2  0 |  1  4  1 | 2 2
. . . x3o3o3o . ♦   5 |   10 |    0   10 |   0    0    5 |   *   *   * 504 |  0   0   3  1 |  0  3  3 | 1 3
----------------+-----+------+-----------+---------------+-----------------+---------------+----------+----
o3o3o3x3o . . . ♦  15 |   60 |   60   20 |  30   15    0 |   6   6   0   0 | 84   *   *  * |  3  0  0 | 3 0
. o3o3x3o3o . . ♦  20 |   90 |   60   60 |  15   30   15 |   0   6   6   0 |  * 252   *  * |  1  2  0 | 2 1
. . o3x3o3o3o . ♦  15 |   60 |   20   60 |   0   15   30 |   0   0   6   6 |  *   * 252  * |  0  2  1 | 1 2
. . . x3o3o3o3o ♦   6 |   15 |    0   20 |   0    0   15 |   0   0   0   6 |  *   *   * 84 |  0  0  3 | 0 3
----------------+-----+------+-----------+---------------+-----------------+---------------+----------+----
o3o3o3x3o3o . . ♦  35 |  210 |  210  140 | 105  105   35 |  21  42  21   0 |  7   7   0  0 | 36  *  * | 2 0
. o3o3x3o3o3o . ♦  35 |  210 |  140  210 |  35  105  105 |   0  21  42  21 |  0   7   7  0 |  * 72  * | 1 1
. . o3x3o3o3o3o ♦  21 |  105 |   35  140 |   0   35  105 |   0   0  21  42 |  0   0   7  7 |  *  * 36 | 0 2
----------------+-----+------+-----------+---------------+-----------------+---------------+----------+----
o3o3o3x3o3o3o . ♦  70 |  560 |  560  560 | 280  420  280 |  56 168 168  56 | 28  56  28  0 |  8  8  0 | 9 *
. o3o3x3o3o3o3o ♦  56 |  420 |  280  560 |  70  280  420 |   0  56 168 168 |  0  28  56 28 |  0  8  8 | * 9
0421 r{3,34,2} [84]
o3o3x3o *c3o3o3o3o - buffy
. . . .    . . . . | 483840 ♦      30 |      30      15      60 |      10      15      60      30      60 |      5     20     30      60      30      30 |    10     20     30     30     15      6 |   10     10    15      6     3 |   5     2    3
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
. . x .    . . . . |      2 | 7257600 |       2       1       4 |       1       2       8       4       6 |      1      4      8      12       6       4 |     4      6     12      8      4      1 |    6      4     8      2     1 |   4     1    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
. o3x .    . . . . |      3 |       3 | 4838400       *       * |       1       1       4       0       0 |      1      4      4       6       0       0 |     4      6      6      4      0      0 |    6      4     4      1     0 |   4     1    1
. . x3o    . . . . |      3 |       3 |       * 2419200       * |       0       2       0       4       0 |      1      0      8       0       6       0 |     4      0     12      0      4      0 |    6      0     8      0     1 |   4     0    2
. . x . *c3o . . . |      3 |       3 |       *       * 9676800 |       0       0       2       1       3 |      0      1      2       6       3       3 |     1      3      6      6      3      1 |    3      3     6      2     1 |   3     1    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
o3o3x .    . . . . ♦      4 |       6 |       4       0       0 | 1209600       *       *       *       * |      1      4      0       0       0       0 |     4      6      0      0      0      0 |    6      4     0      0     0 |   4     1    0
. o3x3o    . . . . ♦      6 |      12 |       4       4       0 |       * 1209600       *       *       * |      1      0      4       0       0       0 |     4      0      6      0      0      0 |    6      0     4      0     0 |   4     0    1
. o3x . *c3o . . . ♦      6 |      12 |       4       0       4 |       *       * 4838400       *       * |      0      1      1       3       0       0 |     1      3      3      3      0      0 |    3      3     3      1     0 |   3     1    1
. . x3o *c3o . . . ♦      6 |      12 |       0       4       4 |       *       *       * 2419200       * |      0      0      2       0       3       0 |     1      0      6      0      3      0 |    3      0     6      0     1 |   3     0    2
. . x . *c3o3o . . ♦      4 |       6 |       0       0       4 |       *       *       *       * 7257600 |      0      0      0       2       1       2 |     0      1      2      4      2      1 |    1      2     4      2     1 |   2     1    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
o3o3x3o    . . . . ♦     10 |      30 |      20      10       0 |       5       5       0       0       0 | 241920      *      *       *       *       * ♦     4      0      0      0      0      0 |    6      0     0      0     0 |   4     0    0
o3o3x . *c3o . . . ♦     10 |      30 |      20       0      10 |       5       0       5       0       0 |      * 967680      *       *       *       * |     1      3      0      0      0      0 |    3      3     0      0     0 |   3     1    0
. o3x3o *c3o . . . ♦     24 |      96 |      32      32      32 |       0       8       8       8       0 |      *      * 604800       *       *       * |     1      0      3      0      0      0 |    3      0     3      0     0 |   3     0    1
. o3x . *c3o3o . . ♦     10 |      30 |      10       0      20 |       0       0       5       0       5 |      *      *      * 2903040       *       * |     0      1      1      2      0      0 |    1      2     2      1     0 |   2     1    1
. . x3o *c3o3o . . ♦     10 |      30 |       0      10      20 |       0       0       0       5       5 |      *      *      *       * 1451520       * |     0      0      2      0      2      0 |    1      0     4      0     1 |   2     0    2
. . x . *c3o3o3o . ♦      5 |      10 |       0       0      10 |       0       0       0       0       5 |      *      *      *       *       * 2903040 |     0      0      0      2      1      1 |    0      1     2      2     1 |   1     1    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
o3o3x3o *c3o . . . ♦     80 |     480 |     320     160     160 |      80      80      80      40       0 |     16     16     10       0       0       0 | 60480      *      *      *      *      * |    3      0     0      0     0 |   3     0    0
o3o3x . *c3o3o . . ♦     20 |      90 |      60       0      60 |      15       0      30       0      15 |      0      6      0       6       0       0 |     * 483840      *      *      *      * |    1      2     0      0     0 |   2     1    0
. o3x3o *c3o3o . . ♦     80 |     480 |     160     160     320 |       0      40      80      80      80 |      0      0     10      16      16       0 |     *      * 181440      *      *      * |    1      0     2      0     0 |   2     0    1
. o3x . *c3o3o3o . ♦     15 |      60 |      20       0      60 |       0       0      15       0      30 |      0      0      0       6       0       6 |     *      *      * 967680      *      * |    0      1     1      1     0 |   1     1    1
. . x3o *c3o3o3o . ♦     15 |      60 |       0      20      60 |       0       0       0      15      30 |      0      0      0       0       6       6 |     *      *      *      * 483840      * |    0      0     2      0     1 |   1     0    2
. . x . *c3o3o3o3o ♦      6 |      15 |       0       0      20 |       0       0       0       0      15 |      0      0      0       0       0       6 |     *      *      *      *      * 483840 |    0      0     0      2     1 |   0     1    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
o3o3x3o *c3o3o . . ♦    720 |    6480 |    4320    2160    4320 |    1080    1080    2160    1080    1080 |    216    432    270     432     216       0 |    27     72     27      0      0      0 | 6720      *     *      *     * |   2     0    0
o3o3x . *c3o3o3o . ♦     35 |     210 |     140       0     210 |      35       0     105       0     105 |      0     21      0      42       0      21 |     0      7      0      7      0      0 |    * 138240     *      *     * |   1     1    0
. o3x3o *c3o3o3o . ♦    240 |    1920 |     640     640    1920 |       0     160     480     480     960 |      0      0     60     192     192     192 |     0      0     12     32     32      0 |    *      * 30240      *     * |   1     0    1
. o3x . *c3o3o3o3o ♦     21 |     105 |      35       0     140 |       0       0      35       0     105 |      0      0      0      21       0      42 |     0      0      0      7      0      7 |    *      *     * 138240     * |   0     1    1
. . x3o *c3o3o3o3o ♦     21 |     105 |       0      35     140 |       0       0       0      35     105 |      0      0      0       0      21      42 |     0      0      0      0      7      7 |    *      *     *      * 69120 |   0     0    2
-------------------+--------+---------+-------------------------+-----------------------------------------+----------------------------------------------+------------------------------------------+--------------------------------+---------------
o3o3x3o *c3o3o3o . ♦  10080 |  120960 |   80640   40320  120960 |   20160   20160   60480   30240   60480 |   4032  12096   7560   24192   12096   12096 |   756   4032   1512   4032   2016      0 |   56    576   126      0     0 | 240     *    *
o3o3x . *c3o3o3o3o ♦     56 |     420 |     280       0     560 |      70       0     280       0     420 |      0     56      0     168       0     168 |     0     28      0     56      0     28 |    0      8     0      8     0 |   * 17280    *
. o3x3o *c3o3o3o3o ♦    672 |    6720 |    2240    2240    8960 |       0     560    2240    2240    6720 |      0      0    280    1344    1344    2688 |     0      0     84    448    448    448 |    0      0    14     64    64 |   *     * 2160

8-honeycombs[edit]

o3o3o3o *c3o3o3o3o3x - goh

o3o3o3o *c3o3o3o3o3x   (N → ∞)

. . . .    . . . . . |  N ♦  240 |  6720 |  60480 | 241920 | 483840 | 483840 | 138240 69120 | 17280 2160
---------------------+----+------+-------+--------+--------+--------+--------+--------------+-----------
. . . .    . . . . x |  2 | 120N ♦    56 |    756 |   4032 |  10080 |  12096 |   4032  2016 |   576  126
---------------------+----+------+-------+--------+--------+--------+--------+--------------+-----------
. . . .    . . . o3x |  3 |    3 | 2240N ♦     27 |    216 |    720 |   1080 |    432   216 |    72   27
---------------------+----+------+-------+--------+--------+--------+--------+--------------+-----------
. . . .    . . o3o3x ♦  4 |    6 |     4 | 15120N ♦     16 |     80 |    160 |     80    40 |    16   10
---------------------+----+------+-------+--------+--------+--------+--------+--------------+-----------
. . . .    . o3o3o3x ♦  5 |   10 |    10 |      5 | 48384N ♦     10 |     30 |     20    10 |     5    5
---------------------+----+------+-------+--------+--------+--------+--------+--------------+-----------
. . . .    o3o3o3o3x ♦  6 |   15 |    20 |     15 |      6 | 80640N ♦      6 |      6     3 |     2    3
---------------------+----+------+-------+--------+--------+--------+--------+--------------+-----------
. . o . *c3o3o3o3o3x ♦  7 |   21 |    35 |     35 |     21 |      7 | 69120N |      2     1 |     1    2
---------------------+----+------+-------+--------+--------+--------+--------+--------------+-----------
. o3o . *c3o3o3o3o3x ♦  8 |   28 |    56 |     70 |     56 |     28 |      8 | 17280N     * |     1    1
. . o3o *c3o3o3o3o3x ♦  8 |   28 |    56 |     70 |     56 |     28 |      8 |      * 8640N |     0    2
---------------------+----+------+-------+--------+--------+--------+--------+--------------+-----------
o3o3o . *c3o3o3o3o3x ♦  9 |   36 |    84 |    126 |    126 |     84 |     36 |      8     0 | 1920N    *
. o3o3o *c3o3o3o3o3x ♦ 16 |  112 |   448 |   1120 |   1792 |   1792 |   1024 |    128   128 |     * 135N

Computation[edit]

The f-vector values, seen on the diagonal, are computed by systematically removing nodes (mirrors) from the Kaleidoscope. The element of a given set of removals is defined by the set of nodes connected to at least one ringed nodes. The number of elements of that type is computed from the full order of the Coxeter group divided by the order of the remaining mirrors. If groups of mirrors are not connected, the order is the product of all such connected groups remaining.

Polyhedra[edit]

Truncated cuboctahedron[edit]

Example truncated cuboctahedron, with all mirrors active, all 1+3+3+1 fundamental domain simplex positions contain elements.

Truncated cuboctahedron
B3 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.png k-face fk f0 f1 f2 k-fig Notes
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png ( ) f0 48 1 1 1 1 1 1 ( )∨( )∨( ) B3 = 48
A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png { } f1 2 24 * * 1 1 0 { } B3/A1 = 24
A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 2 * 24 * 1 0 1 B3/A1 = 24
A1 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 2 * * 24 0 1 1 B3/A1 = 24
A2 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png {6} f2 6 3 3 0 8 * * ( ) B3/A2 = 8*6/6 = 8
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png {4} 4 2 0 2 * 12 * B3/A1/A1 = 48/4 = 12
B2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.png {8} 8 0 4 4 * * 6 B3/B2 = 48/8 = 6

4-polytopes[edit]

5-cell family[edit]

5-cell[edit]

x3o3o3o - pen

A4 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A3 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png ( ) f0 5 4 6 4 {3,3} A4/A3 = 5!/4! = 5
A2A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png { } f1 2 10 3 3 {3} A4/A2A1 = 5!/3!/2 = 10
A2A1 CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3} f2 3 3 10 2 { }
A3 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png {3,3} f3 4 6 4 5 ( ) A4/A3 = 5!/4! = 5
rectified 5-cell[edit]

o3x3o3o - rap

A4 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A2A1 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png ( ) f0 10 6 3 6 3 2 {3}×{ } A4/A2A1 = 5!/3!/2 = 10
A1A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png { } f1 2 30 1 2 2 1 { }∨( ) A4/A1A1 = 5!/4 = 30
A2A1 CDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3} f2 3 3 10 * 2 0 { } A4/A2A1 = 5!/3!/2 = 10
A2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png 3 3 * 20 1 1 A4/A2 = 5!/3! = 20
A3 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png r{3,3} f3 6 12 4 4 5 * ( ) A4/A3 = 5!/4! = 5
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png {3,3} 4 6 0 4 * 5
Truncated 5-cell[edit]

x3x3o3o - tip

A4 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png ( ) f0 20 1 3 3 3 3 1 {3}∨( ) A4/A2 = 5!/3! = 20
A2A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png { } f1 2 10 * 3 0 3 0 {3} A4/A2A1 = 5!/3!/2 = 10
A1A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png 2 * 30 1 2 2 1 { }∨( ) A4/A1A1 = 5!/4 = 30
A2A1 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png t{3} f2 6 3 3 10 * 2 0 { } A4/A2A1 = 5!/3!/2 = 10
A2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png {3} 3 0 3 * 20 1 1 A4/A2 = 5!/3! = 20
A3 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png t{3,3} f3 12 6 12 4 4 5 * ( ) A4/A3 = 5!/4! = 5
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png {3,3} 4 0 6 0 4 * 5
Cantellated 5-cell[edit]

x3o3x3o - srip

A4 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A1A1 CDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png ( ) f0 30 2 4 1 4 2 2 2 2 1 Irr {3}×{ } A4/A1A1 = 5!/4 = 30
A2A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png { } f1 2 30 * 1 2 0 0 2 1 0 { }∨( ) A4/A2A1 = 5!/3!/2 = 30
A1 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 2 * 60 0 1 1 1 1 1 1 ( )∨( )∨( ) A4/A1 = 5!/2 = 60
A2A1 CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3} f2 3 3 0 10 * * * 2 0 0 { } A4/A2A1 = 5!/3!/2 = 10
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png { }×{ } 4 2 2 * 30 * * 1 1 0 A4/A1A1 = 5!/4 = 30
A2 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png {3} 3 0 3 * * 20 * 1 0 1 A4/A2 = 5!/3! = 20
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png 3 0 3 * * * 20 0 1 1 A4/A2 = 5!/3! =20
A3 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png rr{3,3} f3 12 12 12 4 6 4 0 5 * * ( ) A4/A3 = 5!/4! = 5
A2A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png {3}×{ } 6 3 6 0 3 0 2 * 10 * A4/A2A1 = 5!/3!/2 = 10
A3 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png r{3,3} 6 0 12 0 0 4 4 * * 5 A4/A3 = 5!/4! = 5
runcinated 5-cell[edit]

x3o3o3x - spid

A4 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png k-face fk f0 f1 f2 f3 k-fig Notes
A2 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png ( ) f0 20 3 3 3 6 3 1 3 3 1 s{2,6} A4/A2 = 5!/3! = 20
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.png { } f1 2 30 * 2 2 0 1 2 1 0 { }×{ } A4/A1A1 = 5!/4 = 30
CDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 2 * 30 0 2 2 0 1 2 1
A2 CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png {3} f2 3 3 0 20 * * 1 1 0 0 { } A4/A2 = 5!/3! =20
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png { }×{ } 4 2 2 * 30 * 0 1 1 0 A4/A1A1 = 5!/4 = 30
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.png {3} 3 0 3 * * 20 0 0 1 1 A4/A2 = 5!/3! = 20
A3 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png {3,3} f3 4 6 0 4 0 0 5 * * * ( ) A4/A3 = 5!/4! = 5
A2A1 CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png {3}×{ } 6 6 3 2 3 0 * 10 * * A4/A2A1 = 5!/3!/2 = 10
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.png 6 3 6 0 3 2 * * 10 *
A3 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png {3,3} 4 0 6 0 0 4 * * * 5 A4/A3 = 5!/4! = 5
Bitruncated 5-cell[edit]

o3x3x3o - deca

A4 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A1A1 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png ( ) f0 30 2 2 1 4 1 2 2 s{2,4} A4/A1A1 = 5!/4 = 30
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png { } f1 2 30 * 1 2 0 2 1 { }∨( )
CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 2 * 30 0 2 1 1 2
A2A1 CDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3} f2 3 3 0 10 * * 2 0 { } A4/A2A1 = 5!/3!/2 = 10
A2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png t{3} 6 3 3 * 20 * 1 1 A4/A2 = 5!/3! = 20
A2A1 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png {3} 3 0 3 * * 10 0 2 A4/A2A1 = 5!/3!/2 = 10
A3 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png t{3,3} f3 12 12 6 4 4 0 5 * ( ) A4/A3 = 5!/4! = 5
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png 12 6 12 0 4 4 * 5
Runcitruncated 5-cell[edit]

x3x3o3x - prip

A4 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png k-face fk f0 f1 f2 f3 k-fig Notes
A1 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.png ( ) f0 60 1 2 2 2 2 1 2 1 1 2 1 1 irr. { }×{ }∨( ) A4/A1 = 5!/2 = 60
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.png { } f1 2 30 * * 2 2 0 0 0 1 2 1 0 { }×{ } A4/A1A1 = 5!/4 = 30
A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 2 * 60 * 1 0 1 1 0 1 1 0 1 ( )∨( )∨( ) A4/A1 = 5!/2 = 60
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 2 * * 60 0 1 0 1 1 0 1 1 1
A2 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png t{3} f2 6 3 3 0 20 * * * * 1 1 0 0 { } A4/A2 = 5!/3! = 20
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png { }×{ } 4 2 0 2 * 30 * * * 0 1 1 0 A4/A1A1 = 5!/4 = 30
A2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png {3} 3 0 3 0 * * 20 * * 1 0 0 1 A4/A2 = 5!/3! = 20
A1A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png { }×{ } 4 0 2 2 * * * 30 * 0 1 0 1 A4/A1A1 = 5!/4 = 30
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.png {3} 3 0 0 3 * * * * 20 0 0 1 1 A4/A2 = 5!/3! = 20
A3 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png t{3,3} f3 12 6 12 0 4 0 4 0 0 5 * * * ( ) A4/A3 = 5!/4! = 5
A2A1 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png t{3}×{ } 12 6 6 6 2 3 0 3 0 * 10 * * A4/A2A1 = 5!/3!/2 = 10
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.png {3}×{ } 6 3 0 6 0 3 0 0 2 * * 10 *
A3 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png rr{3,3} 12 0 12 12 0 0 4 6 4 * * * 5 A4/A3 = 5!/4! = 5
Runcitruncated 5-cell[edit]

x3x3o3x - prip

A4 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png k-face fk f0 f1 f2 f3 k-fig Notes
A1 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.png ( ) f0 60 1 2 2 2 2 1 2 1 1 2 1 1 irr. { }×{ }∨( ) A4/A1 = 5!/2 = 60
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.png { } f1 2 30 * * 2 2 0 0 0 1 2 1 0 { }×{ } A4/A1A1 = 5!/4 = 30
A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 2 * 60 * 1 0 1 1 0 1 1 0 1 { }∨( ) A4/A1 = 5!/2 = 60
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 2 * * 60 0 1 0 1 1 0 1 1 1
A2 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png t{3} f2 6 3 3 0 20 * * * * 1 1 0 0 { } A4/A2 = 5!/3! = 20
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png { }×{ } 4 2 0 2 * 30 * * * 0 1 1 0 A4/A1A1 = 5!/4 = 30
A2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png {3} 3 0 3 0 * * 20 * * 1 0 0 1 A4/A2 = 5!/3! = 20
A1A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png { }×{ } 4 0 2 2 * * * 30 * 0 1 0 1 A4/A1A1 = 5!/4 = 30
A3 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.png {3} 3 0 0 3 * * * * 20 0 0 1 1 A4/A1A1 = 5!/4 = 30
A3 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png t{3,3} f3 12 6 12 0 4 0 4 0 0 5 * * * ( ) A4/A3 = 5!/4! = 5
A2A1 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png t{3}×{ } 12 6 6 6 2 3 0 3 0 * 10 * * A4/A2A1 = 5!/3!/2 = 10
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.png {3}×{ } 6 3 0 6 0 3 0 0 2 * * 10 *
A3 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png rr{3,3} 12 0 12 12 0 0 4 6 4 * * * 5 A4/A3 = 5!/4! = 5
Omnitruncated 5-cell[edit]

x3x3x3x - gippid

A4 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png k-face fk f0 f1 f2 f3 k-fig Notes
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png ( ) f0 120 1 1 1 1 1 1 1 1 1 1 1 1 1 1 irr {3,3} A4 = 5! = 120
A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png { } f1 2 60 * * * 1 1 1 0 0 0 1 1 1 0 { }∨( ) A4/A1 = 5!/2 = 60
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 2 * 60 * * 1 0 0 1 1 0 1 1 0 1
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 2 * * 60 * 0 1 0 1 0 1 1 0 1 1
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 2 * * * 60 0 0 1 0 1 1 0 1 1 1
A2 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png t{3} f2 6 3 3 0 0 20 * * * * * 1 1 0 0 { } A4/A2 = 5!/3! = 20
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png { }×{ } 4 2 0 2 0 * 30 * * * * 1 0 1 0 A4/A1A1 = 5!/4 = 30
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 4 2 0 0 2 * * 30 * * * 0 1 1 0
A2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png t{3} 6 0 3 3 0 * * * 20 * * 1 0 0 1 A4/A2 = 5!/3! = 20
A1A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png { }×{ } 4 0 2 0 2 * * * * 30 * 0 1 0 1 A4/A1A1 = 5!/4 = 30
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.png t{3} 6 0 0 3 3 * * * * * 20 0 0 1 1 A4/A2 = 5!/3! = 20
A3 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png tr{3,3} f3 24 12 12 12 0 4 6 0 4 0 0 5 * * * ( ) A4/A3 = 5!/4! = 5
A2A1 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png t{3}×{ } 12 6 6 0 6 2 0 3 0 3 0 * 10 * * A4/A2A1 = 5!/3!/2 = 10
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.png 12 6 0 6 6 0 3 3 0 0 2 * * 10 *
A3 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png tr{3,3} 24 0 12 12 12 0 0 0 4 6 4 * * * 5 A4/A3 = 5!/4! = 5

24-cell family[edit]

24-cell[edit]

x3o4o3o - ico

F4 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
B3 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png ( ) f0 24 8 12 6 {4,3} F4/B3 = 1152/48 = 24
A2A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png { } f1 2 96 3 3 {3} F4/A2A1 = 1152/3!/2 = 96
CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3} f2 3 3 96 2 { }
B3 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png {3,4} f3 6 12 8 24 ( ) F4/B3 = 1152/48 = 24
Rectified 24-cell[edit]

o3x4o3o - rico

F4 CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A2A1 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png ( ) f0 96 6 3 6 3 2 {3}×{ } F4/A2A1 = 1152/3!/2 = 96
A1A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png { } f1 2 288 1 2 2 1 { }∨( ) F4/A1A1 = 1152/4 = 288
A2A1 CDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3} f2 3 3 96 * 2 0 { } F4/A2A1 = 1152/3!/2 = 96
B2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png {4} 4 4 * 144 1 1 F4/B2 = 1152/8 = 144
B3 CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png r{4,3} f3 12 24 8 6 24 * ( ) F4/B3 = 1152/48 = 24
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png {4,3} 8 12 0 6 * 24
Truncated 24-cell[edit]

x3x4o3o - tico

F4 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png ( ) f0 192 1 3 3 3 3 1 {3}∨( ) F4/A2 = 1152/3! = 192
A2A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png { } f1 2 96 * 3 0 3 0 {3} F4/A2A1 = 1152/3!/2 = 96
A1A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png 2 * 288 1 2 2 1 { }∨( ) F4/A1A1 = 1152/4 = 288
A2A1 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png t{3} f2 6 3 3 96 * 2 0 { } F4/A2A1 = 1152/3!/2 = 96
B2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png {4} 4 0 4 * 144 1 1 F4/B2 = 1152/8 = 144
B3 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png t{3,4} f3 24 12 24 8 6 24 * ( ) F4/B3 = 1152/48 = 24
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png {4,3} 8 0 12 0 6 * 24
Cantellated 24-cell[edit]

x3o4x3o - sric

F4 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A1A1 CDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png ( ) f0 288 2 4 1 4 2 2 2 2 1 irr {3}×{ } F4/A1A1 = 1152/4 = 288
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png { } f1 2 288 * 1 2 0 0 2 1 0 { }∨( )
A1 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 2 * 576 0 1 1 1 1 1 1 ( )∨( )∨( ) F4/A1 = 1152/2 = 576
A2A1 CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png f2 3 3 0 96 * * * 2 0 0 { } F4/A2A1 = 1152/3!/2 = 96
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png { }×{ } 4 2 2 * 288 * * 1 1 0 F4/A1A1 = 1152/4 = 288
B2 CDel node x.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node x.png {4} 4 0 4 * * 144 * 1 0 1 F4/B2 = 1152/8 = 144
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png {3} 3 0 3 * * * 192 0 1 1 F4/A2 = 1152/3! = 192
B3 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node x.png rr{4,3} f3 24 24 24 8 12 6 0 24 * * ( ) F4/B3 = 1152/48 = 24
A2A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png {3}×{ } 6 3 6 0 3 0 2 * 96 * F4/A2A1 = 1152/3!/2 = 96
B3 CDel node x.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png r{4,3} 12 0 24 0 0 6 8 * * 24 F4/B3 = 1152/48 = 24
Runcinated 24-cell[edit]

x3o4o3x - spic

F4 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png k-face fk f0 f1 f2 f3 k-fig Notes
B2 CDel node x.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png ( ) f0 144 4 4 4 8 4 1 4 4 1 elong s{2,8} F4/B2 = 1152/8 = 144
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.png { } f1 2 288 * 2 2 0 1 2 1 0 { }∨( ) F4/A1A1 = 1152/4 = 288
CDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 2 * 288 0 2 2 0 1 2 1
A2 CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png {3} f2 3 3 0 192 * * 1 1 0 0 { } F4/A1 = 1152/3! = 192
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png { }×{ } 4 2 2 * 288 * 0 1 1 0 F4/A1A1 = 1152/4 = 288
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.png {3} 3 0 3 * * 192 0 0 1 1 F4/A2 = 1152/3! = 192
B3 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png {3,4} f3 6 12 0 8 0 0 24 * * * ( ) F4/B3 = 1152/48 = 24
A2A1 CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png {3}×{ } 6 6 3 2 3 0 * 96 * * F4/A2A1 = 1152/3!/2 = 96
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.png 6 3 6 0 3 2 * * 96 *
B3 CDel node x.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png {3,4} 6 0 12 0 0 8 * * * 24 F4/B3 = 1152/48 = 24
Bitruncated 24-cell[edit]

o3x4x3o - cont

F4 CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A1A1 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png ( ) f0 288 2 2 1 4 1 2 2 s{2,4} F4/A1A1 = 288
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png { } f1 2 288 * 1 2 0 2 1 { }∨( )
CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 2 * 288 0 2 1 1 2
A2A1 CDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3} f2 3 3 0 96 * * 2 0 { } F4/A2A1 = 1152/6/2 = 96
B2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node x.png t{4} 8 4 4 * 144 * 1 1 F4/B2 = 1152/8 = 144
A2A1 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png {3} 3 0 3 * * 96 0 2 F4/A2A1 = 1152/6/2 = 96
B3 CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node x.png t{4,3} f3 24 24 12 8 6 0 24 * ( ) F4/B3 = 1152/48 = 24
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png 24 12 24 0 6 8 * 24
Cantitruncated 24-cell[edit]

x3x4x3o - grico

F4 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A1 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png f0 576 1 1 2 1 2 2 1 2 1 1 F4/A1 = 1152/2 = 576
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png f1 2 288 * * 1 2 0 0 2 1 0 F4/A1A1A1A1 = 1152/4 = 288
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png 2 * 288 * 1 0 2 0 2 0
A1 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 2 * * 576 0 1 1 1 1 1 1 F4/A1 = 1152/2 = 576
A2A1 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png f2 6 3 3 0 96 * * * 2 0 0 F4/A2A1 = 1152/3!/2 = 96
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 4 2 0 2 * 288 * * 1 1 0 F4/A1A1 = 1152/4 = 288
B2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node x.png 8 0 4 4 * * 144 * 1 0 1 F4/B2 = 1152/8 = 144
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png 3 0 0 3 * * * 192 0 1 1 F4/A2 = 1152/3! = 192
B3 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node x.png f3 48 24 24 24 8 12 6 0 24 * * F4/B3 = 1152/48 = 24
A2A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png 6 3 0 6 0 3 0 2 * 96 * F4/A2A1 = 1152/3!/2 = 96
B3 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png 24 0 12 24 0 0 6 8 * * 24 F4/B3 = 1152/48 = 24
Runcitruncated 24-cell[edit]

x3x4o3x - prico

F4 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png k-face fk f0 f1 f2 f3 k-fig Notes
A1 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.png f0 576 1 2 2 2 2 1 2 1 1 2 1 1 F4 = 1152
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node x.png f1 2 288 * * 2 2 0 0 0 1 2 1 0 F4/A1 = 1152/2 = 288
A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 2 * 576 * 1 0 1 1 0 1 1 0 1 F4/A1 = 1152/2 = 576
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 2 * * 576 0 1 0 1 1 0 1 1 1
A2 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png f2 6 3 3 0 192 * * * * 1 1 0 0 F4/A2 = 1152/3! = 192
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 4 2 0 2 * 288 * * * 0 1 1 0 F4/A1A1 = 1152/4 = 288
B2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png 4 0 4 0 * * 144 * * 1 0 0 1 F4/B2 = 1152/8 = 144
A1A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 4 0 2 2 * * * 288 * 0 1 0 1 F4/A1A1 = 1152/4 = 288
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.png 3 0 0 3 * * * * 192 0 0 1 1 F4/A2 = 1152/3! = 192
B3 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png f3 24 12 24 0 8 0 6 0 0 24 * * * F4/B3 = 1152/48 = 24
A2A1 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 12 6 6 6 2 3 0 3 0 * 96 * * F4/A2A1 = 1152/3!/2 = 96
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.png 6 3 0 6 0 3 0 0 2 * * 96 *
B3 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png 24 0 24 24 0 0 6 12 8 * * * 24 F4/B3 = 1152/48 = 24
Omnitruncated 24-cell[edit]

x3x4x3x - gippic

F4 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.png k-face fk f0 f1 f2 f3 k-fig Notes
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png ( ) f0 1152 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Irr. {3,3} F4 = 1152
A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png { } f1 2 576 * * * 1 1 1 0 0 0 1 1 1 0 ( )∨( )∨( ) F4/A1 = 1152/2 = 576
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 2 * 576 * * 1 0 0 1 1 0 1 1 0 1
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 2 * * 576 * 0 1 0 1 0 1 1 0 1 1
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 2 * * * 576 0 0 1 0 1 1 0 1 1 1
A2 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png t{3} f2 6 3 3 0 0 192 * * * * * 1 1 0 0 { } F4/A2 = 1152/3! = 192
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png { }×{ } 4 2 0 2 0 * 288 * * * * 1 0 1 0 F4/A1A1 = 1152/4 = 288
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 4 2 0 0 2 * * 288 * * * 0 1 1 0
B2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node x.png t{4} 8 0 4 4 0 * * * 144 * * 1 0 0 1 F4/B2 = 1152/8 = 144
A1A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png { }×{ } 4 0 2 0 2 * * * * 288 * 0 1 0 1 F4/A1A1 = 1152/4 = 288
A2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.png t{3} 6 0 0 3 3 * * * * * 192 0 0 1 1 F4/A2 = 1152/3! = 192
B3 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node x.png tr{4,3} f3 48 24 24 24 0 8 12 0 6 0 0 24 * * * ( ) F4/B3 = 1152/48 = 24
A2A1 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png t{3}×{ } 12 6 6 0 6 2 0 3 0 3 0 * 96 * * F4/A2A1 = 1152/3!/2 = 96
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.png 12 6 0 6 6 0 3 3 0 0 2 * * 96 *
B3 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.png tr{4,3} 48 0 24 24 24 0 0 0 6 12 8 * * * 24 F4/B3 = 1152/ 48 = 24
Snub 24-cell[edit]

Example: snub 24-cell

½F4 CDel node h.pngCDel 3.pngCDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
demi( CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png ) ( ) f0 96 3 6 3 9 3 3 1 4 I-3
( CDel node x.pngCDel 2.pngCDel node h.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png ) { } f1 2 144 * 0 2 2 1 1 2 { }||{ }
sefa( CDel node h.pngCDel 3.pngCDel node h.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png ) 2 * 288 1 2 0 2 0 1 { }∨( )
( CDel node h.pngCDel 3.pngCDel node h.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png ) {3} f2 3 0 3 96 * * 2 0 0 { }
sefa( CDel node h.pngCDel 3.pngCDel node h.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png ) 3 1 2 * 288 * 1 0 1
sefa( CDel node x.pngCDel 2.pngCDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png ) 3 3 0 * * 96 0 1 1
( CDel node h.pngCDel 3.pngCDel node h.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node x.png ) {3,5} f3 12 6 24 8 12 0 24 * * ( )
( CDel node x.pngCDel 2.pngCDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png ) {3,3} 4 6 0 0 0 4 * 24 *
sefa( CDel node h.pngCDel 3.pngCDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png ) 4 3 3 0 3 1 * * 96

Omnitruncated tesseract[edit]

Example on omnitruncated tesseract. An omnitruncated 4-polytope will have 2^4-1 or 15 types of elements.

B4 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.png k-face fk f0 f1 f2 f3 k-fig Notes
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png ( ) f0 384 1 1 1 1 1 1 1 1 1 1 1 1 1 1 {3,3} B4 = 384
A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png { } f1 2 192 * * * 1 1 1 0 0 0 1 1 1 0 ( )∨( )∨( ) B4/A1 = 192
A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png { } 2 * 192 * * 1 0 0 1 1 0 1 1 0 1 B4/A1 = 192
A1 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png { } 2 * * 192 * 0 1 0 1 0 1 1 0 1 1 B4/A1 = 192
A1 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png { } 2 * * * 192 0 0 1 0 1 1 0 1 1 1 B4/A1 = 192
A2 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png {6} f2 6 3 3 0 0 64 * * * * * 1 1 0 0 { } B4/A2 = 64
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png {4} 4 2 0 2 0 * 96 * * * * 1 0 1 0 B4/A1A1 = 96
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png {4} 4 2 0 0 2 * * 96 * * * 0 1 1 0 B4/A1A1 = 96
A2 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png {6} 6 0 3 3 0 * * * 64 * * 1 0 0 1 B4/A2 = 64
A1A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png {4} 4 0 2 0 2 * * * * 96 * 0 1 0 1 B4/A1A1 = 96
B2 CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.png {8} 8 0 0 4 4 * * * * * 48 0 0 1 1 B4/B2 = 48
A3 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png tr{3,3} f3 24 12 12 12 0 4 6 0 4 0 0 16 * * * ( ) B4/A3 = 16
A2A1 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png {6}×{ } 12 6 6 0 6 2 0 3 0 3 0 * 32 * * B4/A2A1 = 32
B2A1 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.png {8}×{ } 16 8 0 8 8 0 4 4 0 0 2 * * 24 * B4/B2A1 = 24
B3 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.png tr{4,3} 48 0 24 24 24 0 0 0 8 12 6 * * * 8 B4/B3 = 8

600-cell[edit]

H4 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
H3 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node.png ( ) f0 120 12 30 20 {3,5} CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node.png H4/H3 = 14400/120 = 120
A1H2 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.png { } f1 2 720 5 5 {5} CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 5.pngCDel node.png H4/H2A1 = 14400/10/2 = 720
A2A1 CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3} f2 3 3 1200 2 { } CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png H4/A2A1 = 14400/6/2 = 1200
A3 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png {3,3} f3 4 6 4 600 ( ) CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png H4/A3 = 14400/24 = 600

120-cell[edit]

H4 CDel node 1.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 k-fig Notes
A3 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png ( ) f0 600 4 6 4 {3,3} CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png H4/A3 = 14400/24 = 600
A1A2 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png { } f1 2 720 3 3 {3} CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png H4/A2A1 = 14400/6/2 = 1200
H2A1 CDel node 1.pngCDel 5.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {5} f2 5 5 1200 2 { } CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png H4/H2A1 = 14400/10/2 = 720
H3 CDel node 1.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png {5,3} f3 20 30 12 120 ( ) CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png H4/H3 = 14400/120 = 120

5-polytopes[edit]

0_31[edit]

Example rectified 5-simplex

A5 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 f4 k-fig notes
A3A1 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png ( ) f0 15 8 4 12 6 8 4 2 { }×{3,3} CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png A5/A3A1 = 6!/4!/2 = 15
A2A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png { } f1 2 60 1 3 3 3 3 1 ( )∨{3} CDel node.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png A5/A2A1 = 6!/3!/2 = 60
A2A2 CDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png r{3} f2 3 3 20 * 3 0 3 0 {3} CDel node 1.pngCDel 3.pngCDel node.png A5/A2A2 = 6!/3!/3! =20
A2A1 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3} 3 3 * 60 1 2 2 1 ( )×{ } CDel node.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node 1.png A5/A2A1 = 6!/3!/2 = 60
A3A1 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png r{3,3} f3 6 12 4 4 15 * 2 0 { } CDel node 1.png A5/A3A1 = 6!/4!/2 = 15
A3 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png {3,3} 4 6 0 4 * 30 1 1 ( )∨( ) CDel node.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node.png A5/A3 = 6!/4! = 30
A4 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png r{3,3,3} f4 10 30 10 20 5 5 6 * ( ) CDel node.png A5/A4 = 6!/5! = 6
A4 CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png {3,3,3} 5 10 0 10 0 5 * 6 CDel node.png A5/A4 = 6!/5! = 6

0_22[edit]

Example birectified 5-simplex

A5 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png k-face fk f0 f1 f2 f3 f4 k-fig notes
A2A2 CDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png ( ) f0 20 9 9 9 3 9 3 3 3 {3}×{3} CDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png A5/A2A2 = 6!/3!/3! = 20
A1A1A1 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png { } f1 2 90 2 2 1 4 1 2 2 { }∨{ } CDel node 1.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node 1.png A5/A1A1A1 = 6!/8 = 90
A2A1 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3} f2 3 3 60 * 1 2 0 2 1 { }∨( ) CDel node 1.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node.png A5/A2A1 = 6!/3!/2 = 60
A2A1 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png 3 3 * 60 0 2 1 1 2 ( )∨{ } CDel node.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node 1.png
A3A1 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3,3} f3 4 6 4 0 15 * * 2 0 { } CDel node 1.png A5/A3A1 = 6!/4!/2 = 15
A3 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png r{3,3} 6 12 4 4 * 30 * 1 1 CDel node.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node.png A5/A3 = 6!/4! = 30
A3A1 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png {3,3} 4 6 0 4 * * 15 0 2 CDel node 1.png A5/A3A1 = 6!/4!/2 = 15
A4 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png r{3,3,3} f4 10 30 20 10 5 5 0 6 * ( ) CDel node.png A5/A4 = 6!/5! = 6
A4 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png 10 30 10 20 0 5 5 * 6

1_21[edit]

Example 5-demicube:

D5 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png
CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
k-face fk f0 f1 f2 f3 f4 k-fig notes
A4 CDel nodea x.pngCDel 2.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png ( ) f0 16 10 30 10 20 5 5 r{3,3,3} D5/A4 = 16*5!/5! = 16
A2A1A1 CDel nodea 1.pngCDel 2.pngCDel nodes x0.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png { } f1 2 80 6 3 6 3 2 {3}×{ } D5/A2A1A1 = 16*5!/3!/4 = 80
A2A1 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3} f2 3 3 160 1 2 2 1 { }∨( ) D5/A2A1 = 16*5!/3!/2 = 160
A3A1 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png h{4,3} f3 4 6 4 40 * 2 0 { } D5/A3A1 = 16*5!/4!/2 = 40
A3 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png {3,3} 4 6 4 * 80 1 1 D5/A3 = 16*5!/4! = 80
D4 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png h{4,3,3} f4 8 24 32 8 8 10 * ( ) D5/D4 = 16*5!/8/4! = 10
A4 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,3,3} 5 10 10 0 5 * 16 D5/A4 = 16*5!/5! = 16

6-polytopes[edit]

1_31[edit]

Example 6-demicube

D6 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png
CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
k-face fk f0 f1 f2 f3 f4 f5 k-fig notes
A4 CDel nodea x.pngCDel 2.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png ( ) f0 32 15 60 20 60 15 30 6 6 r{3,3,3,3} D6/A4 = 32*6!/5! = 32
A3A1A1 CDel nodea 1.pngCDel 2.pngCDel nodes x0.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png { } f1 2 240 8 4 12 6 8 4 2 {}×{3,3} D6/A3A1A1 = 32*6!/4!/4 = 240
A3A2 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3} f2 3 3 640 1 3 3 3 3 1 {3}∨( ) D6/A3A2 = 32*6!/4!/3! = 640
A3A1 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png h{4,3} f3 4 6 4 160 * 3 0 3 0 {3} D6/A3A1 = 32*6!/4!/2 = 160
A3A2 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3,3} 4 6 4 * 480 1 2 2 1 {}∨( ) D6/A3A2 = 32*6!/4!/3! = 480
D4A1 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png h{4,3,3} f4 8 24 32 8 8 60 * 2 0 { } D6/D4A1 = 32*6!/8/4!/2 = 60
A4 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png {3,3,3} 5 10 10 0 5 * 192 1 1 D6/A4 = 32*6!/5! = 192
D5 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png h{4,3,3,3} f5 16 80 160 40 80 10 16 12 * ( ) D6/D5 = 32*6!/16/5! = 12
A5 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,3,3,3} 6 15 20 0 15 0 6 * 32 D6/A5 = 32*6!/6! = 32

2_21[edit]

Example on 2_21 polytope:

E6 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png k-face fk f0 f1 f2 f3 f4 f5 k-fig notes
D5 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png ( ) f0 27 16 80 160 80 40 16 10 h{4,3,3,3} E6/D5 = 51840/1920 = 27
A4A1 CDel nodea 1.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png { } f1 2 216 10 30 20 10 5 5 r{3,3,3} E6/A4A1 = 51840/120/2 = 216
A2A2A1 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodes x0.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3} f2 3 3 720 6 6 3 2 3 {3}×{ } E6/A2A2A1 = 51840/6/6/2 = 720
A3A1 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3,3} f3 4 6 4 1080 2 1 1 2 { }∨( ) E6/A3A1 = 51840/24/2 = 1080
A4 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png {3,3,3} f4 5 10 10 5 432 * 1 1 { } E6/A4 = 51840/120 = 432
A4A1 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 5 10 10 5 * 216 0 2 E6/A4A1 = 51840/120/2 = 216
A5 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,3,3,3} f5 6 15 20 15 6 0 72 * ( ) E6/A5 = 51840/720 = 72
D5 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png {3,3,3,4} 10 40 80 80 16 16 * 27 E6/D5 = 51840/1920 = 27

1_22[edit]

Example on 1_22 polytope:

E6 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png k-face fk f0 f1 f2 f3 f4 f5 k-fig notes
A5 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png ( ) f0 72 20 90 60 60 15 15 30 6 6 r{3,3,3} CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png E6/A5 = 72*6!/6! = 72
A2A2A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodes x1.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png { } f1 2 720 9 9 9 3 3 9 3 3 {3}×{3} CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 2.pngCDel 2.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png E6/A2A2A1 = 72*6!/3!/3!/2 = 720
A2A1A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 01.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3} f2 3 3 2160 2 2 1 1 4 2 2 { }∨{ } CDel node 1.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node 1.png E6/A2A1A1 = 72*6!/3!/4 = 2160
A3A1 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 01l.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3,3} f3 4 6 4 1080 * 1 0 2 2 1 { }∨( ) CDel node 1.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node.png E6/A3A1 = 72*6!/4!/2 = 1080
CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 01r.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 4 6 4 * 1080 0 1 2 1 2 CDel node.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node 1.png
A4A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 01r.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,3,3} f4 5 10 10 5 0 216 * * 2 0 { } CDel node 1.png E6/A4A1 = 72*6!/5!/2 = 216
CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01l.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 5 10 10 0 5 * 216 * 0 2
D4 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png {3,3,4} 8 24 32 8 8 * * 270 1 1 CDel node.pngCDel 2.pngCDel join.pngCDel 2.pngCDel node.png E6/D4 = 72*6!/8/4! = 270
D5 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png h{4,3,3,3} f5 16 80 160 80 40 16 0 10 27 * ( ) CDel node.png E6/D5 = 72*6!/16/5! = 27
CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 16 80 160 40 80 0 16 10 * 27

0_221[edit]

Example Rectified 1_22 polytope

E6 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png k-face fk f0 f1 f2 f3 f4 f5 k-fig notes
A2A2A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodes x0.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png ( ) f0 720 18 18 18 9 6 18 9 6 9 6 3 6 9 3 2 3 3 {3}×{3}×{ } E6/A2A2A1 = 72*6!/3!/3!/2 = 720
A1A1A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodes 1x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png { } f1 2 6480 2 2 1 1 4 2 1 2 2 1 2 4 1 1 2 2 { }∨{ }∨( ) E6/A1A1A1 = 72*6!/8 = 6480
A2A1 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3} f2 3 3 4320 * * 1 2 1 0 0 2 1 1 2 0 1 2 1 Sphenoid E6/A2A1 = 72*6!/3!/2 = 4320
CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 3 3 * 4320 * 0 2 0 1 1 1 0 2 2 1 1 1 2
A2A1A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 10.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 3 3 * * 2160 0 0 2 0 2 0 1 0 4 1 0 2 2 { }∨{ } E6/A2A1A1 = 72*6!/3!/4 = 2160
A2A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3,3} f3 4 6 4 0 0 1080 * * * * 2 1 0 0 0 1 2 0 { }∨( ) E6/A2A1 = 72*6!/3!/2 = 1080
A3 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png r{3,3} 6 12 4 4 0 * 2160 * * * 1 0 1 1 0 1 1 1 {3} E6/A3 = 72*6!/4! = 2160
A3A1 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 6 12 4 0 4 * * 1080 * * 0 1 0 2 0 0 2 1 { }∨( ) E6/A3A1 = 72*6!/4!/2 = 1080
CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,3} 4 6 0 4 0 * * * 1080 * 0 0 2 0 1 1 0 2
CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png r{3,3} 6 12 0 4 4 * * * * 1080 0 0 0 2 1 0 1 2
A4 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png r{3,3,3} f4 10 30 20 10 0 5 5 0 0 0 432 * * * * 1 1 0 { } E6/A4 = 72*6!/5! = 432
A4A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 10 30 20 0 10 5 0 5 0 0 * 216 * * * 0 2 0 E6/A4A1 = 72*6!/5!/2 = 216
A4 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 10 30 10 20 0 0 5 0 5 0 * * 432 * * 1 0 1 E6/A4 = 72*6!/5! = 432
D4 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png h{4,3,3} 24 96 32 32 32 0 8 8 0 8 * * * 270 * 0 1 1 E6/D4 = 72*6!/8/4! = 270
A4A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png r{3,3,3} 10 30 0 20 10 0 0 0 5 5 * * * * 216 0 0 2 E6/A4A1 = 72*6!/5!/2 = 216
A5 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 2r{3,3,3,3} f5 20 90 60 60 0 15 30 0 15 0 6 0 6 0 0 72 * * ( ) E6/A5 = 72*6!/6! = 72
D5 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png rh{4,3,3,3} 80 480 320 160 160 80 80 80 0 40 16 16 0 10 0 * 27 * E6/D5 = 72*6!/16/5! = 27
CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 80 480 160 320 160 0 80 40 80 80 0 0 16 10 16 * * 27

Omnitruncated 6-simplex[edit]

Example: Omnitruncated 6-simplex BIG TEST!

A6 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png k-face fk f0 f1 f2 f3 f4 f5 k-fig notes
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 5040 2 2 2 2 2 2 2 1 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 2 2 2
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 2 5040 * * 1 1 1 1 1 0 0 0 0 1 1 1 2 1 1 2 1 0 0 1 1 2 1 2 1 1 1 0 1 2 2
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 2 * 5040 * 1 0 0 1 0 1 1 1 0 1 1 2 1 0 1 0 1 1 2 1 2 1 2 1 1 1 0 1 2 1 2
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 2 * * 5040 0 1 1 0 0 1 1 0 1 1 1 0 0 2 1 1 1 2 1 2 1 1 1 1 0 2 1 1 2 2 1
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 6 3 3 0 1680 * * * * * * * * 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 2
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 4 2 0 2 * 2520 * * * * * * * 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 2 1
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 4 2 0 2 * * 2520 * * * * * * 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 2 1
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 4 2 2 0 * * * 2520 * * * * * 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 2
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 4 4 0 0 * * * * 1260 * * * * 0 0 0 2 0 0 2 0 0 0 0 0 2 0 2 1 0 1 0 0 2 2
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 6 0 3 3 * * * * * 1680 * * * 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 2 1 1
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 4 0 2 2 * * * * * * 2520 * * 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 0 1 2 1 1
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 4 0 4 0 * * * * * * * 1260 * 0 0 2 0 0 0 0 0 0 2 0 2 0 2 0 1 0 0 1 2 0 2
CDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 6 0 0 6 * * * * * * * * 840 0 0 0 0 2 0 0 0 2 0 2 0 0 0 0 0 2 1 1 2 2 0
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 24 12 12 12 4 6 0 0 0 4 0 0 0 420 * * * * * * * * * 1 1 1 0 0 0 0 0 0 1 1 1
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 12 6 6 6 2 0 3 0 0 0 3 0 0 * 840 * * * * * * * * 1 0 0 1 1 0 0 0 0 1 1 1
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 12 6 12 0 2 0 0 3 0 0 0 3 0 * * 840 * * * * * * * 0 1 0 1 0 1 0 0 0 1 0 2
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 12 12 6 0 2 0 0 3 3 0 0 0 0 * * * 840 * * * * * * 0 0 1 0 1 1 0 0 0 0 1 2
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 12 6 0 12 0 3 3 0 0 0 0 0 2 * * * * 840 * * * * * 1 0 0 0 0 0 1 1 0 1 2 0
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 8 4 4 4 0 2 0 2 0 0 2 0 0 * * * * * 1260 * * * * 0 1 0 0 1 0 1 0 0 1 1 1
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 8 8 0 4 0 2 2 0 2 0 0 0 0 * * * * * * 1260 * * * 0 0 1 0 1 0 0 1 0 0 2 1
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png 12 6 6 6 0 0 3 3 0 2 0 0 0 * * * * * * * 840 * * 0 0 1 1 0 0 1 0 0 1 1 1
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 24 0 12 24 0 0 0 0 0 4 6 0 4 * * * * * * * * 420 * 1 0 0 0 0 0 1 0 1 2 1 0
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 12 0 12 6 0 0 0 0 0 2 3 3 0 * * * * * * * * * 8 40 0 1 0 1 0 0 0 0 1 2 0 1
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.png 120 60 60 120 20 30 30 0 0 20 30 0 20 5 10 0 0 10 0 0 0 5 0 84 * * * * * * * * 1 1 0
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.png 48 24 48 24 8 12 0 12 0 8 12 12 0 2 0 4 0 0 6 0 0 0 4 * 210 * * * * * * * 1 0 1
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 48 48 24 24 8 12 12 12 12 8 0 0 0 2 0 0 4 0 0 6 4 0 0 * * 210 * * * * * * 0 1 1
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png 36 18 36 18 6 0 9 9 0 6 9 9 0 0 3 3 0 0 0 0 3 0 3 * * * 280 * * * * * 1 0 1
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 24 24 12 12 4 6 6 6 6 0 6 0 0 0 2 0 2 0 3 3 0 0 0 * * * * 420 * * * * 0 1 1
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.png 36 36 36 0 12 0 0 18 9 0 0 9 0 0 0 6 6 0 0 0 0 0 0 * * * * * 140 * * * 0 0 2
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png 48 24 24 48 0 12 12 12 0 8 12 0 8 0 0 0 0 4 6 0 4 2 0 * * * * * * 210 * * 1 1 0
CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 24 24 0 24 0 12 12 0 6 0 0 0 4 0 0 0 0 4 0 6 0 0 0 * * * * * * * 210 * 0 2 0
CDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png 120 0 120 120 0 0 0 0 0 40 60 30 20 0 0 0 0 0 0 0 0 10 20 * * * * * * * * 42 2 0 0
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.png 720 360 720 720 120 180 180 180 0 240 360 180 120 30 60 60 0 60 90 0 60 60 1 20 6 15 0 20 0 0 15 0 6 14 * *
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png 240 240 120 240 40 120 120 60 60 40 60 0 40 10 20 0 20 40 30 60 20 10 0 2 0 5 0 10 0 5 10 0 * 42 *
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.png 144 144 144 72 48 36 36 72 36 24 36 36 0 6 12 24 24 0 18 18 12 0 12 0 3 3 4 6 4 0 0 0 * * 70

7-polytopes[edit]

1_41[edit]

Example on 7-demicube:

D7 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png
CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
k-face fk f0 f1 f2 f3 f4 f5 f6 k-fig notes
A6 CDel nodea x.pngCDel 2.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png ( ) f0 64 21 105 35 140 35 105 21 42 7 7 r{3,3,3,3,3} D7/A6 = 64*7!/7! = 64
A4A1A1 CDel nodea 1.pngCDel 2.pngCDel nodes x0.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png { } f1 2 672 10 5 20 10 20 10 10 5 2 { }×{3,3,3} D7/A4A1A1 = 64*7!/5!/4 = 672
A3A2 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3} f2 3 3 2240 1 4 4 6 6 4 4 1 {3,3}∨( ) D7/A3A2 = 64*7!/4!/3! = 2240
A3A3 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png h{4,3} f3 4 6 4 560 * 4 0 6 0 4 0 {3,3} D7/A3A3 = 64*7!/4!/4! = 560
A3A2 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,3} 4 6 4 * 2240 1 3 3 3 3 1 {3}∨( ) D7/A3A2 = 64*7!/4!/3! = 2240
D4A2 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png h{4,3,3} f4 8 24 32 8 8 280 * 3 0 3 0 {3} D7/D4A2 = 64*7!/8/4!/2 = 280
A4A1 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3,3,3} 5 10 10 0 5 * 1344 1 2 2 1 { }∨( ) D7/A4A1 = 64*7!/5!/2 = 1344
D5A1 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png h{4,3,3,3} f5 16 80 160 40 80 10 16 84 * 2 0 { } D7/D5A1 = 64*7!/16/5!/2 = 84
A5 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png {3,3,3,3} 6 15 20 0 15 0 6 * 448 1 1 D7/A5 = 64*7!/6! = 448
D6 CDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png h{4,3,3,3,3} f6 32 240 640 160 480 60 192 12 32 14 * ( ) D7/D6 = 64*7!/32/6! = 14
A6 CDel nodea 1.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,3,3,3,3} 7 21 35 0 35 0 21 0 7 * 64 D7/A6 = 64*7!/7! = 64

3_21[edit]

Example on 3_21 polytope:

E7 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png k-face fk f0 f1 f2 f3 f4 f5 f6 k-fig notes
E6 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png ( ) f0 56 27 216 720 1080 432 216 72 27 221 E7/E6 = 72x8!/72x6! = 56
D5A1 CDel nodea 1.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png { } f1 2 756 16 80 160 80 40 16 10 5-demicube E7/D5A1 = 72x8!/16/5!/2 = 756
A4A2 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3} f2 3 3 4032 10 30 20 10 5 5 rectified 5-cell E7/A4A2 = 72x8!/5!/2 = 4032
A3A2A1 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodes x0.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,3} f3 4 6 4 10080 6 6 3 2 3 triangular prism E7/A3A2A1 = 72x8!/4!/3!/2 = 10080
A4A1 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3,3,3} f4 5 10 10 5 12096 2 1 1 2 isosceles triangle E7/A4A1 = 72x8!/5!/2 = 12096
A5A1 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3,3,3,3} f5 6 15 20 15 6 4032 * 1 1 { } E7/A5A1 = 72x8!/6!/2 = 4032
A5 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 6 15 20 15 6 * 2016 0 2 E7/A5 = 72x8!/6! = 2016
A6 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,3,3,3,3} f6 7 21 35 35 21 10 0 576 * ( ) E7/A6 = 72x8!/7! = 576
D6 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png {3,3,3,3,4} 12 60 160 240 192 32 32 * 126 E7/D6 = 72x8!/32/6! = 126

2_31[edit]

Example on 2_31 polytope:

E7 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png k-face fk f0 f1 f2 f3 f4 f5 f6 k-fig notes
D6 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png ( ) f0 126 32 240 640 160 480 60 192 12 32 6-demicube E7/D6 = 72x8!/32/6! = 126
A5A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea 1.png { } f1 2 2016 15 60 20 60 15 30 6 6 rectified 5-simplex E7/A5A1 = 72x8!/6!/2 = 2016
A3A2A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodes x0.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png {3} f2 3 3 10080 8 4 12 6 8 4 2 tetrahedral prism E7/A3A2A1 = 72x8!/4!/3!/2 = 10080
A3A2 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png {3,3} f3 4 6 4 20160 1 3 3 3 3 1 tetrahedron E7/A3A2 = 72x8!/4!/3! = 20160
A4A2 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png {3,3,3} f4 5 10 10 5 4032 * 3 0 3 0 {3} E7/A4A2 = 72x8!/5!/3! = 4032
A4A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png 5 10 10 5 * 12096 1 2 2 1 Isosceles triangle E7/A4A1 = 72x8!/5!/2 = 12096
D5A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png {3,3,3,4} f5 10 40 80 80 16 16 756 * 2 0 { } E7/D5A1 = 72x8!/32/5! = 756
A5 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png {3,3,3,3} 6 15 20 15 0 6 * 4032 1 1 E7/A5 = 72x8!/6! = 72*8*7 = 4032
E6 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png {3,3,32,1} f6 27 216 720 1080 216 432 27 72 56 * ( ) E7/E6 = 72x8!/72x6! = 8*7 = 56
A6 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png {3,3,3,3,3} 7 21 35 35 0 21 0 7 * 576 E7/A6 = 72x8!/7! = 72×8 = 576

1_32[edit]

Example on 1_32 polytope:

E7 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png k-face fk f0 f1 f2 f3 f4 f5 f6 k-fig notes
A6 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 0x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png ( ) f0 576 35 210 140 210 35 105 105 21 42 21 7 7 2r{3,3,3,3,3} E7/A6 = 72*8!/7! = 576
A3A2A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodes x1.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png { } f1 2 10080 12 12 18 4 12 12 6 12 3 4 3 {3,3}×{3} E7/A3A2A1 = 72*8!/4!/3!/2 = 10080
A2A2A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 01.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3} f2 3 3 40320 2 3 1 6 3 3 6 1 3 2 { }∨{3} E7/A2A2A1 = 72*8!/3!/3!/2 = 40320
A3A2 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 01r.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png {3,3} f3 4 6 4 20160 * 1 3 0 3 3 0 3 1 {3}∨( ) E7/A3A2 = 72*8!/4!/3! = 20160
A3A1A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 01l.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 4 6 4 * 30240 0 2 2 1 4 1 2 2 Phyllic disphenoid E7/A3A1A1 = 72*8!/4!/4 = 30240
A4A2 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 01r.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,3,3} f4 5 10 10 5 0 4032 * * 3 0 0 3 0 {3} E7/A4A2 = 72*8!/5!/3! = 4032
D4A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png {3,3,4} 8 24 32 8 8 * 7560 * 1 2 0 2 1 { }∨( ) E7/D4A1 = 72*8!/8/4!/2 = 7560
A4A1 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01l.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3,3,3} 5 10 10 0 5 * * 12096 0 2 1 1 2 E7/A4A1 = 72*8!/5!/2 = 12096
D5A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png h{4,3,3,3} f5 16 80 160 80 40 16 10 0 756 * * 2 0 { } E7/D5A1 = 72*8!/16/5!/2 = 756
D5 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 16 80 160 40 80 0 10 16 * 1512 * 1 1 E7/D5 = 72*8!/16/5! = 1512
A5A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01l.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png {3,3,3,3,3} 6 15 20 0 15 0 0 6 * * 2016 0 2 E7/A5A1 = 72*8!/6!/2 = 2016
E6 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3,32,2} f6 72 720 2160 1080 1080 216 270 216 27 27 0 56 * ( ) E7/E6 = 72*8!/72/6! = 56
D6 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png h{4,3,3,3,3} 32 240 640 160 480 0 60 192 0 12 32 * 126 E7/D6 = 72*8!/32/6! = 126

0_321[edit]

Example on rectified 1_32 polytope:

E7 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png k-face fk f0 f1 f2 f3 f4 f5 f6 k-fig notes
A3A2A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodes x0.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.png ( ) f0 10080 24 24 12 36 8 12 36 18 24 4 12 18 24 12 6 6 8 12 6 3 4 2 3 {3,3}×{3}×{ } E7/A3A2A1 = 72*8!/4!/3!/2 = 10080
A2A1A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodes 1x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png { } f1 2 120960 2 1 3 1 2 6 3 3 1 3 6 6 3 1 3 3 6 2 1 3 1 2 ( )∨{3}∨{ } E7/A2A1A1 = 72*8!/3!/4 = 120960
A2A2 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 01 f2 3 3 80640 * * 1 1 3 0 0 1 3 3 3 0 0 3 3 3 1 0 3 1 1 {3}∨( )∨( ) E7/A2A2 = 72*8!/3!/3! = 80640
A2A2A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 10.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 3 3 * 40320 * 0 2 0 3 0 1 0 6 0 3 0 3 0 6 0 1 3 0 2 {3}∨{ } E7/A2A2A1 = 72*8!/3!/3!/2 = 40320
A2A1A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 3 3 * * 120960 0 0 2 1 2 0 1 2 4 2 1 1 2 4 2 1 2 1 2 { }∨{ }∨( ) E7/A2A1A1 = 72*8!/3!/4 = 120960
A3A2 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 02 f3 4 6 4 0 0 20160 * * * * 1 3 0 0 0 0 3 3 0 0 0 3 1 0 {3}∨( ) E7/A3A2 = 72*8!/4!/3! = 20160
CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 011 6 12 4 4 0 * 20160 * * * 1 0 3 0 0 0 3 0 3 0 0 3 0 1
A3A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 6 12 4 0 4 * * 60480 * * 0 1 1 2 0 0 1 2 2 1 0 2 1 1 Sphenoid E7/A3A1 = 72*8!/4!/2 = 60480
A3A1A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 6 12 0 4 4 * * * 30240 * 0 0 2 0 2 0 1 0 4 0 1 2 0 2 { }∨{ } E7/A3A1A1 = 72*8!/4!/2/2 = 30240
A3A1 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 02 4 6 0 0 4 * * * * 60480 0 0 0 2 1 1 0 1 2 2 1 1 1 2 Sphenoid E7/A3A1 = 72*8!/4!/2 = 60480
A4A2 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 021 f4 10 30 20 10 0 5 5 0 0 0 4032 * * * * * 3 0 0 0 0 3 0 0 {3} E7/A4A2 = 72*8!/5!/3! = 4032
A4A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 10 30 20 0 10 5 0 5 0 0 * 12096 * * * * 1 2 0 0 0 2 1 0 { }∨() E7/A4A1 = 72*8!/5!/2 = 12096
D4A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 0111 24 96 32 32 32 0 8 8 8 0 * * 7560 * * * 1 0 2 0 0 2 0 1 E7/D4A1 = 72*8!/8/4!/2 = 7560
A4 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 021 10 30 10 0 20 0 0 5 0 5 * * * 24192 * * 0 1 1 1 0 1 1 1 ( )∨( )∨( ) E7/A4 = 72*8!/5! = 34192
A4A1 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 10 30 0 10 20 0 0 0 5 5 * * * * 12096 * 0 0 2 0 1 1 0 2 { }∨() E7/A4A1 = 72*8!/5!/2 = 12096
CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 03 5 10 0 0 10 0 0 0 0 5 * * * * * 12096 0 0 0 2 1 0 1 2
D5A1 CDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 0211 f5 80 480 320 160 160 80 80 80 40 0 16 16 10 0 0 0 756 * * * * 2 0 0 { } E7/D5A1 = 72*8!/16/5!/2 = 756
A5 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 022 20 90 60 0 60 15 0 30 0 15 0 6 0 6 0 0 * 4032 * * * 1 1 0 E7/A5 = 72*8!/6! = 4032
D5 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 0211 80 480 160 160 320 0 40 80 80 80 0 0 10 16 16 0 * * 1512 * * 1 0 1 E7/D5 = 72*8!/16/5! = 1512
A5 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 031 15 60 20 0 60 0 0 15 0 30 0 0 0 6 0 6 * * * 4032 * 0 1 1 E7/A5 = 72*8!/6! = 4032
A5A1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.png 15 60 0 20 60 0 0 0 15 30 0 0 0 0 6 6 * * * * 2016 0 0 2 E7/A5A1 = 72*8!/6!/2 = 2016
E6 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 0221 f6 720 6480 4320 2160 4320 1080 1080 2160 1080 1080 216 432 270 432 216 0 27 72 27 0 0 56 * * ( ) E7/E6 = 72*8!/72/6! = 56
A6 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodes 1x.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 032 35 210 140 0 210 35 0 105 0 105 0 21 0 42 0 21 0 7 0 7 0 * 576 * E7/A6 = 72*8!/7! = 576
D6 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.png 0311 240 1920 640 640 1920 0 160 480 480 960 0 0 60 192 192 192 0 0 12 32 32 * * 126 E7/D6 = 72*8!/32/6! = 126

8-polytopes[edit]

8-cube[edit]

Example on 8-cube. A regular n-polytope will have n types of elements, one for each dimension.

B8 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png k-face fk f0 f1 f2 f3 f4 f5 f6 f7 k-fig notes
A7 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png ( ) f0 256 8 28 56 70 56 28 8 {3,3,3,3,3,3} B8/A7 = 2^8*8!/8! = 256
A6A1 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node 1.png { } f1 2 1024 7 21 35 35 21 7 {3,3,3,3,3} B8/A6A1 = 2^8*8!/7!/2 = 1024
A5B2 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node 1.png {4} f2 4 4 1792 6 15 20 15 6 {3,3,3,3} B8/A5B2 = 2^8*8!/6!/4/2 = 1792
A4B3 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png {4,3} f3 8 12 6 1792 5 10 10 5 {3,3,3} B8/A4B3 = 2^8*8!/5!/8/3! = 1792
A3B4 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png {4,3,3} f4 16 32 24 8 1120 4 6 4 {3,3} B8/A3B4 = 2^8*8!/4!/2^4/4! = 1120
A2B5 CDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png {4,3,3,3} f5 32 80 80 40 10 448 3 3 {3} B8/A2B5 = 2^8*8!/3!/2^5/5! = 448
A1B6 CDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png {4,3,3,3,3} f6 64 192 240 160 60 12 112 2 { } B8/A1B6 = 2^8*8!/2/2^6/6!= 112
B7 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png {4,3,3,3,3,3} f7 128 448 672 560 280 84 14 16 ( ) B8/B7 = 2^8*8!/2^7/7! = 16

8-orthoplex[edit]

B8 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png k-face fk f0 f1 f2 f3 f4 f5 f6 f7 k-fig notes
B7 CDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png ( ) f0 16 14 84 280 560 672 448 128 {3,3,3,3,3,4} B8/B7 = 2^8*8!/2^7/7! = 16
A1B6 CDel node 1.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png { } f1 2 112 12 60 160 240 192 64 {3,3,3,3,4} B8/A1B6 = 2^8*8!/2/2^6/6! = 112
A2B5 CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png {3} f2 3 3 448 10 40 80 80 32 {3,3,3,4} B8/A2B5 = 2^8*8!/3!/2^5/5! = 448
A3B4 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png {3,3} f3 4 6 4 1120 8 24 32 16 {3,3,4} B8/A3B4 = 2^8*8!/4!/2^4/4! = 1120
A4B3 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png {3,3,3} f4 5 10 10 5 1792 6 12 8 {3,4} B8/A4B3 = 2^8*8!/5!/8/3! = 1792
A5B2 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.png {3,3,3,3} f5 6 15 20 15 6 1792 4 4 {4} B8/A5B2 = 2^8*8!/6!/4/2 = 1792
A6A1 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.pngCDel 2.pngCDel node.png {3,3,3,3,3} f6 7 21 35 35 21 7 1024 2 { } B8/A6A1 = 2^8*8!/7!/2 = 1024
A7 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node x.png {3,3,3,3,3,3} f7 8 28 56 70 56 28 8 256 ( ) B8/A7 = 2^8*8!/8! = 256

4_21[edit]

Example on 4_21 polytope:

E8 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png k-face fk f0 f1 f2 f3 f4 f5 f6 f7 k-fig notes
E7 CDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png ( ) f0 240 56 756 4032 10080 12096 4032 2016 576 126 321 E8/E7 = 192x10!/72x8! = 240
A1E6 CDel nodea 1.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png { } f1 2 6720 27 216 720 1080 432 216 72 27 221 E8/A1E6 = 192x10!/2/72x6! = 6720
A2D5 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea x.pngCDel 2.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png {3} f2 3 3 60480 16 80 160 80 40 16 10 121 E8/A2D5 = 192x10!/6/2^4/5! = 60480
A3A4 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png