Uniform 7-polytope

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Graphs of three regular and related uniform polytopes
7-simplex t0.svg
7-simplex
7-simplex t1.svg
Rectified 7-simplex
7-simplex t01.svg
Truncated 7-simplex
7-simplex t02.svg
Cantellated 7-simplex
7-simplex t03.svg
Runcinated 7-simplex
7-simplex t04.svg
Stericated 7-simplex
7-simplex t05.svg
Pentellated 7-simplex
7-simplex t06.svg
Hexicated 7-simplex
7-cube t6.svg
7-orthoplex
7-cube t56.svg
Truncated 7-orthoplex
7-cube t5.svg
Rectified 7-orthoplex
7-cube t46.svg
Cantellated 7-orthoplex
7-cube t36.svg
Runcinated 7-orthoplex
7-cube t26.svg
Stericated 7-orthoplex
7-cube t16.svg
Pentellated 7-orthoplex
7-cube t06.svg
Hexicated 7-cube
7-cube t05.svg
Pentellated 7-cube
7-cube t04.svg
Stericated 7-cube
7-cube t02.svg
Cantellated 7-cube
7-cube t03.svg
Runcinated 7-cube
7-cube t0.svg
7-cube
7-cube t01.svg
Truncated 7-cube
7-cube t1.svg
Rectified 7-cube
7-demicube t0 D7.svg
7-demicube
7-demicube t01 D7.svg
Truncated 7-demicube
7-demicube t02 D7.svg
Cantellated 7-demicube
7-demicube t03 D7.svg
Runcinated 7-demicube
7-demicube t04 D7.svg
Stericated 7-demicube
7-demicube t05 D7.svg
Pentellated 7-demicube
E7 graph.svg
321
Gosset 2 31 polytope.svg
231
Gosset 1 32 petrie.svg
132

In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope ridge being shared by exactly two 6-polytope facets.

A uniform 7-polytope is one which is vertex-transitive, and constructed from uniform 6-polytope facets.

Regular 7-polytopes[edit]

Regular 7-polytopes are represented by the Schläfli symbol {p,q,r,s,t,u} with u {p,q,r,s,t} 6-polytopes facets around each 4-face.

There are exactly three such convex regular 7-polytopes:

  1. {3,3,3,3,3,3} - 7-simplex
  2. {4,3,3,3,3,3} - 7-cube
  3. {3,3,3,3,3,4} - 7-orthoplex

There are no nonconvex regular 7-polytopes.

Characteristics[edit]

The topology of any given 7-polytope is defined by its Betti numbers and torsion coefficients.[1]

The value of the Euler characteristic used to characterise polyhedra does not generalize usefully to higher dimensions, whatever their underlying topology. This inadequacy of the Euler characteristic to reliably distinguish between different topologies in higher dimensions led to the discovery of the more sophisticated Betti numbers.[1]

Similarly, the notion of orientability of a polyhedron is insufficient to characterise the surface twistings of toroidal polytopes, and this led to the use of torsion coefficients.[1]

Uniform 7-polytopes by fundamental Coxeter groups[edit]

Uniform 7-polytopes with reflective symmetry can be generated by these four Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams:

# Coxeter group Regular and semiregular forms Uniform count
1 A7 [36] 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.png 71
2 B7 [4,35] CDel node.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 127 + 32
3 D7 [33,1,1] CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png 95 (0 unique)
4 E7 [33,2,1] CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 127
Prismatic finite Coxeter groups
# Coxeter group Coxeter diagram
6+1
1 A6A1 [35]×[ ] 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.png
2 BC6A1 [4,34]×[ ] CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.png
3 D6A1 [33,1,1]×[ ] CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.png
4 E6A1 [32,2,1]×[ ] CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 2.pngCDel nodea.png
5+2
1 A5I2(p) [3,3,3]×[p] CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.png
2 BC5I2(p) [4,3,3]×[p] CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.png
3 D5I2(p) [32,1,1]×[p] CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.png
5+1+1
1 A5A12 [3,3,3]×[ ]2 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
2 BC5A12 [4,3,3]×[ ]2 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
3 D5A12 [32,1,1]×[ ]2 CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
4+3
1 A4A3 [3,3,3]×[3,3] CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
2 A4B3 [3,3,3]×[4,3] CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
3 A4H3 [3,3,3]×[5,3] CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.png
4 BC4A3 [4,3,3]×[3,3] CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5 BC4B3 [4,3,3]×[4,3] CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
6 BC4H3 [4,3,3]×[5,3] CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.png
7 H4A3 [5,3,3]×[3,3] CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
8 H4B3 [5,3,3]×[4,3] CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
9 H4H3 [5,3,3]×[5,3] CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.png
10 F4A3 [3,4,3]×[3,3] CDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
11 F4B3 [3,4,3]×[4,3] CDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
12 F4H3 [3,4,3]×[5,3] CDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.png
13 D4A3 [31,1,1]×[3,3] CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
14 D4B3 [31,1,1]×[4,3] CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
15 D4H3 [31,1,1]×[5,3] CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.png
4+2+1
1 A4I2(p)A1 [3,3,3]×[p]×[ ] CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.png
2 BC4I2(p)A1 [4,3,3]×[p]×[ ] CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.png
3 F4I2(p)A1 [3,4,3]×[p]×[ ] CDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.png
4 H4I2(p)A1 [5,3,3]×[p]×[ ] CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.png
5 D4I2(p)A1 [31,1,1]×[p]×[ ] CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.png
4+1+1+1
1 A4A13 [3,3,3]×[ ]3 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
2 BC4A13 [4,3,3]×[ ]3 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
3 F4A13 [3,4,3]×[ ]3 CDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
4 H4A13 [5,3,3]×[ ]3 CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
5 D4A13 [31,1,1]×[ ]3 CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
3+3+1
1 A3A3A1 [3,3]×[3,3]×[ ] CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.png
2 A3B3A1 [3,3]×[4,3]×[ ] CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.png
3 A3H3A1 [3,3]×[5,3]×[ ] CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.png
4 BC3B3A1 [4,3]×[4,3]×[ ] CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.png
5 BC3H3A1 [4,3]×[5,3]×[ ] CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.png
6 H3A3A1 [5,3]×[5,3]×[ ] CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.png
3+2+2
1 A3I2(p)I2(q) [3,3]×[p]×[q] CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.pngCDel q.pngCDel node.png
2 BC3I2(p)I2(q) [4,3]×[p]×[q] CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.pngCDel q.pngCDel node.png
3 H3I2(p)I2(q) [5,3]×[p]×[q] CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.pngCDel q.pngCDel node.png
3+2+1+1
1 A3I2(p)A12 [3,3]×[p]×[ ]2 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
2 BC3I2(p)A12 [4,3]×[p]×[ ]2 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
3 H3I2(p)A12 [5,3]×[p]×[ ]2 CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
3+1+1+1+1
1 A3A14 [3,3]×[ ]4 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
2 BC3A14 [4,3]×[ ]4 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
3 H3A14 [5,3]×[ ]4 CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
2+2+2+1
1 I2(p)I2(q)I2(r)A1 [p]×[q]×[r]×[ ] CDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.pngCDel q.pngCDel node.pngCDel 2.pngCDel node.pngCDel r.pngCDel node.pngCDel 2.pngCDel node.png
2+2+1+1+1
1 I2(p)I2(q)A13 [p]×[q]×[ ]3 CDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.pngCDel q.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
2+1+1+1+1+1
1 I2(p)A15 [p]×[ ]5 CDel node.pngCDel p.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png
1+1+1+1+1+1+1
1 A17 [ ]7 CDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.png

The A7 family[edit]

The A7 family has symmetry of order 40320 (8 factorial).

There are 71 (64+8-1) forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings. All 71 are enumerated below. Norman Johnson's truncation names are given. Bowers names and acronym are also given for cross-referencing.

See also a list of A7 polytopes for symmetric Coxeter plane graphs of these polytopes.

# Coxeter-Dynkin diagram Truncation
indices
Johnson name
Bowers name (and acronym)
Basepoint Element counts
6 5 4 3 2 1 0
1 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 1.png t0 7-simplex (oca) (0,0,0,0,0,0,0,1) 8 28 56 70 56 28 8
2 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1 Rectified 7-simplex (roc) (0,0,0,0,0,0,1,1) 16 84 224 350 336 168 28
3 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png t2 Birectified 7-simplex (broc) (0,0,0,0,0,1,1,1) 16 112 392 770 840 420 56
4 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png t3 Trirectified 7-simplex (he) (0,0,0,0,1,1,1,1) 16 112 448 980 1120 560 70
5 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1 Truncated 7-simplex (toc) (0,0,0,0,0,0,1,2) 16 84 224 350 336 196 56
6 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2 Cantellated 7-simplex (saro) (0,0,0,0,0,1,1,2) 44 308 980 1750 1876 1008 168
7 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,2 Bitruncated 7-simplex (bittoc) (0,0,0,0,0,1,2,2) 588 168
8 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,3 Runcinated 7-simplex (spo) (0,0,0,0,1,1,1,2) 100 756 2548 4830 4760 2100 280
9 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,3 Bicantellated 7-simplex (sabro) (0,0,0,0,1,1,2,2) 2520 420
10 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png t2,3 Tritruncated 7-simplex (tattoc) (0,0,0,0,1,2,2,2) 980 280
11 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,4 Stericated 7-simplex (sco) (0,0,0,1,1,1,1,2) 2240 280
12 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,4 Biruncinated 7-simplex (sibpo) (0,0,0,1,1,1,2,2) 4200 560
13 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png t2,4 Tricantellated 7-simplex (stiroh) (0,0,0,1,1,2,2,2) 3360 560
14 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,5 Pentellated 7-simplex (seto) (0,0,1,1,1,1,1,2) 1260 168
15 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,5 Bistericated 7-simplex (sabach) (0,0,1,1,1,1,2,2) 3360 420
16 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 1.png t0,6 Hexicated 7-simplex (suph) (0,1,1,1,1,1,1,2) 336 56
17 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2 Cantitruncated 7-simplex (garo) (0,0,0,0,0,1,2,3) 1176 336
18 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,3 Runcitruncated 7-simplex (patto) (0,0,0,0,1,1,2,3) 4620 840
19 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,3 Runcicantellated 7-simplex (paro) (0,0,0,0,1,2,2,3) 3360 840
20 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,2,3 Bicantitruncated 7-simplex (gabro) (0,0,0,0,1,2,3,3) 2940 840
21 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,4 Steritruncated 7-simplex (cato) (0,0,0,1,1,1,2,3) 7280 1120
22 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,4 Stericantellated 7-simplex (caro) (0,0,0,1,1,2,2,3) 10080 1680
23 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,2,4 Biruncitruncated 7-simplex (bipto) (0,0,0,1,1,2,3,3) 8400 1680
24 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,3,4 Steriruncinated 7-simplex (cepo) (0,0,0,1,2,2,2,3) 5040 1120
25 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,3,4 Biruncicantellated 7-simplex (bipro) (0,0,0,1,2,2,3,3) 7560 1680
26 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png t2,3,4 Tricantitruncated 7-simplex (gatroh) (0,0,0,1,2,3,3,3) 3920 1120
27 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,5 Pentitruncated 7-simplex (teto) (0,0,1,1,1,1,2,3) 5460 840
28 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,5 Penticantellated 7-simplex (tero) (0,0,1,1,1,2,2,3) 11760 1680
29 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,2,5 Bisteritruncated 7-simplex (bacto) (0,0,1,1,1,2,3,3) 9240 1680
30 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,3,5 Pentiruncinated 7-simplex (tepo) (0,0,1,1,2,2,2,3) 10920 1680
31 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,3,5 Bistericantellated 7-simplex (bacroh) (0,0,1,1,2,2,3,3) 15120 2520
32 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,4,5 Pentistericated 7-simplex (teco) (0,0,1,2,2,2,2,3) 4200 840
33 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,6 Hexitruncated 7-simplex (puto) (0,1,1,1,1,1,2,3) 1848 336
34 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,6 Hexicantellated 7-simplex (puro) (0,1,1,1,1,2,2,3) 5880 840
35 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,3,6 Hexiruncinated 7-simplex (puph) (0,1,1,1,2,2,2,3) 8400 1120
36 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,3 Runcicantitruncated 7-simplex (gapo) (0,0,0,0,1,2,3,4) 5880 1680
37 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,4 Stericantitruncated 7-simplex (cagro) (0,0,0,1,1,2,3,4) 16800 3360
38 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,3,4 Steriruncitruncated 7-simplex (capto) (0,0,0,1,2,2,3,4) 13440 3360
39 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,3,4 Steriruncicantellated 7-simplex (capro) (0,0,0,1,2,3,3,4) 13440 3360
40 CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,2,3,4 Biruncicantitruncated 7-simplex (gibpo) (0,0,0,1,2,3,4,4) 11760 3360
41 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,5 Penticantitruncated 7-simplex (tegro) (0,0,1,1,1,2,3,4) 18480 3360
42 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,3,5 Pentiruncitruncated 7-simplex (tapto) (0,0,1,1,2,2,3,4) 27720 5040
43 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,3,5 Pentiruncicantellated 7-simplex (tapro) (0,0,1,1,2,3,3,4) 25200 5040
44 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,2,3,5 Bistericantitruncated 7-simplex (bacogro) (0,0,1,1,2,3,4,4) 22680 5040
45 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,4,5 Pentisteritruncated 7-simplex (tecto) (0,0,1,2,2,2,3,4) 15120 3360
46 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,4,5 Pentistericantellated 7-simplex (tecro) (0,0,1,2,2,3,3,4) 25200 5040
47 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png t1,2,4,5 Bisteriruncitruncated 7-simplex (bicpath) (0,0,1,2,2,3,4,4) 20160 5040
48 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,3,4,5 Pentisteriruncinated 7-simplex (tacpo) (0,0,1,2,3,3,3,4) 15120 3360
49 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,6 Hexicantitruncated 7-simplex (pugro) (0,1,1,1,1,2,3,4) 8400 1680
50 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,3,6 Hexiruncitruncated 7-simplex (pugato) (0,1,1,1,2,2,3,4) 20160 3360
51 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,3,6 Hexiruncicantellated 7-simplex (pugro) (0,1,1,1,2,3,3,4) 16800 3360
52 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,4,6 Hexisteritruncated 7-simplex (pucto) (0,1,1,2,2,2,3,4) 20160 3360
53 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,4,6 Hexistericantellated 7-simplex (pucroh) (0,1,1,2,2,3,3,4) 30240 5040
54 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,5,6 Hexipentitruncated 7-simplex (putath) (0,1,2,2,2,2,3,4) 8400 1680
55 CDel node.pngCDel 3.pngCDel node.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 t0,1,2,3,4 Steriruncicantitruncated 7-simplex (gecco) (0,0,0,1,2,3,4,5) 23520 6720
56 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,3,5 Pentiruncicantitruncated 7-simplex (tegapo) (0,0,1,1,2,3,4,5) 45360 10080
57 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,4,5 Pentistericantitruncated 7-simplex (tecagro) (0,0,1,2,2,3,4,5) 40320 10080
58 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,3,4,5 Pentisteriruncitruncated 7-simplex (tacpeto) (0,0,1,2,3,3,4,5) 40320 10080
59 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,3,4,5 Pentisteriruncicantellated 7-simplex (tacpro) (0,0,1,2,3,4,4,5) 40320 10080
60 CDel node.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.pngCDel 3.pngCDel node.png t1,2,3,4,5 Bisteriruncicantitruncated 7-simplex (gabach) (0,0,1,2,3,4,5,5) 35280 10080
61 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,3,6 Hexiruncicantitruncated 7-simplex (pugopo) (0,1,1,1,2,3,4,5) 30240 6720
62 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,4,6 Hexistericantitruncated 7-simplex (pucagro) (0,1,1,2,2,3,4,5) 50400 10080
63 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,3,4,6 Hexisteriruncitruncated 7-simplex (pucpato) (0,1,1,2,3,3,4,5) 45360 10080
64 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png t0,2,3,4,6 Hexisteriruncicantellated 7-simplex (pucproh) (0,1,1,2,3,4,4,5) 45360 10080
65 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,5,6 Hexipenticantitruncated 7-simplex (putagro) (0,1,2,2,2,3,4,5) 30240 6720
66 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,3,5,6 Hexipentiruncitruncated 7-simplex (putpath) (0,1,2,2,3,3,4,5) 50400 10080
67 CDel node.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.pngCDel 3.pngCDel node 1.png t0,1,2,3,4,5 Pentisteriruncicantitruncated 7-simplex (geto) (0,0,1,2,3,4,5,6) 70560 20160
68 CDel node 1.pngCDel 3.pngCDel node.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 t0,1,2,3,4,6 Hexisteriruncicantitruncated 7-simplex (pugaco) (0,1,1,2,3,4,5,6) 80640 20160
69 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,3,5,6 Hexipentiruncicantitruncated 7-simplex (putgapo) (0,1,2,2,3,4,5,6) 80640 20160
70 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png t0,1,2,4,5,6 Hexipentistericantitruncated 7-simplex (putcagroh) (0,1,2,3,3,4,5,6) 80640 20160
71 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.pngCDel 3.pngCDel node 1.png t0,1,2,3,4,5,6 Omnitruncated 7-simplex (guph) (0,1,2,3,4,5,6,7) 141120 40320

The B7 family[edit]

The B7 family has symmetry of order 645120 (7 factorial x 27).

There are 127 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings. Johnson and Bowers names.

See also a list of B7 polytopes for symmetric Coxeter plane graphs of these polytopes.

# Coxeter-Dynkin diagram
t-notation
Name (BSA) Base point Element counts
6 5 4 3 2 1 0
1 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0{3,3,3,3,3,4}
7-orthoplex (zee) (0,0,0,0,0,0,1)√2 128 448 672 560 280 84 14
2 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1{3,3,3,3,3,4}
Rectified 7-orthoplex (rez) (0,0,0,0,0,1,1)√2 142 1344 3360 3920 2520 840 84
3 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2{3,3,3,3,3,4}
Birectified 7-orthoplex (barz) (0,0,0,0,1,1,1)√2 142 1428 6048 10640 8960 3360 280
4 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t3{4,3,3,3,3,3}
Trirectified 7-cube (sez) (0,0,0,1,1,1,1)√2 142 1428 6328 14560 15680 6720 560
5 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2{4,3,3,3,3,3}
Birectified 7-cube (bersa) (0,0,1,1,1,1,1)√2 142 1428 5656 11760 13440 6720 672
6 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1{4,3,3,3,3,3}
Rectified 7-cube (rasa) (0,1,1,1,1,1,1)√2 142 980 2968 5040 5152 2688 448
7 CDel node 1.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
t0{4,3,3,3,3,3}
7-cube (hept) (0,0,0,0,0,0,0)√2 + (1,1,1,1,1,1,1) 14 84 280 560 672 448 128
8 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1{3,3,3,3,3,4}
Truncated 7-orthoplex (Taz) (0,0,0,0,0,1,2)√2 142 1344 3360 4760 2520 924 168
9 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2{3,3,3,3,3,4}
Cantellated 7-orthoplex (Sarz) (0,0,0,0,1,1,2)√2 226 4200 15456 24080 19320 7560 840
10 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2{3,3,3,3,3,4}
Bitruncated 7-orthoplex (Botaz) (0,0,0,0,1,2,2)√2 4200 840
11 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,3{3,3,3,3,3,4}
Runcinated 7-orthoplex (Spaz) (0,0,0,1,1,1,2)√2 23520 2240
12 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,3{3,3,3,3,3,4}
Bicantellated 7-orthoplex (Sebraz) (0,0,0,1,1,2,2)√2 26880 3360
13 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2,3{3,3,3,3,3,4}
Tritruncated 7-orthoplex (Totaz) (0,0,0,1,2,2,2)√2 10080 2240
14 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,4{3,3,3,3,3,4}
Stericated 7-orthoplex (Scaz) (0,0,1,1,1,1,2)√2 33600 3360
15 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,4{3,3,3,3,3,4}
Biruncinated 7-orthoplex (Sibpaz) (0,0,1,1,1,2,2)√2 60480 6720
16 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2,4{4,3,3,3,3,3}
Tricantellated 7-cube (Strasaz) (0,0,1,1,2,2,2)√2 47040 6720
17 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2,3{4,3,3,3,3,3}
Tritruncated 7-cube (Tatsa) (0,0,1,2,2,2,2)√2 13440 3360
18 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,5{3,3,3,3,3,4}
Pentellated 7-orthoplex (Staz) (0,1,1,1,1,1,2)√2 20160 2688
19 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,5{4,3,3,3,3,3}
Bistericated 7-cube (Sabcosaz) (0,1,1,1,1,2,2)√2 53760 6720
20 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,4{4,3,3,3,3,3}
Biruncinated 7-cube (Sibposa) (0,1,1,1,2,2,2)√2 67200 8960
21 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,3{4,3,3,3,3,3}
Bicantellated 7-cube (Sibrosa) (0,1,1,2,2,2,2)√2 40320 6720
22 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,2{4,3,3,3,3,3}
Bitruncated 7-cube (Betsa) (0,1,2,2,2,2,2)√2 9408 2688
23 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,6{4,3,3,3,3,3}
Hexicated 7-cube (Suposaz) (0,0,0,0,0,0,1)√2 + (1,1,1,1,1,1,1) 5376 896
24 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,5{4,3,3,3,3,3}
Pentellated 7-cube (Stesa) (0,0,0,0,0,1,1)√2 + (1,1,1,1,1,1,1) 20160 2688
25 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,4{4,3,3,3,3,3}
Stericated 7-cube (Scosa) (0,0,0,0,1,1,1)√2 + (1,1,1,1,1,1,1) 35840 4480
26 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,3{4,3,3,3,3,3}
Runcinated 7-cube (Spesa) (0,0,0,1,1,1,1)√2 + (1,1,1,1,1,1,1) 33600 4480
27 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,2{4,3,3,3,3,3}
Cantellated 7-cube (Sersa) (0,0,1,1,1,1,1)√2 + (1,1,1,1,1,1,1) 16128 2688
28 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1{4,3,3,3,3,3}
Truncated 7-cube (Tasa) (0,1,1,1,1,1,1)√2 + (1,1,1,1,1,1,1) 142 980 2968 5040 5152 3136 896
29 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2{3,3,3,3,3,4}
Cantitruncated 7-orthoplex (Garz) (0,1,2,3,3,3,3)√2 8400 1680
30 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3{3,3,3,3,3,4}
Runcitruncated 7-orthoplex (Potaz) (0,1,2,2,3,3,3)√2 50400 6720
31 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,3{3,3,3,3,3,4}
Runcicantellated 7-orthoplex (Parz) (0,1,1,2,3,3,3)√2 33600 6720
32 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,3{3,3,3,3,3,4}
Bicantitruncated 7-orthoplex (Gebraz) (0,0,1,2,3,3,3)√2 30240 6720
33 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,4{3,3,3,3,3,4}
Steritruncated 7-orthoplex (Catz) (0,0,1,1,1,2,3)√2 107520 13440
34 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,4{3,3,3,3,3,4}
Stericantellated 7-orthoplex (Craze) (0,0,1,1,2,2,3)√2 141120 20160
35 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,4{3,3,3,3,3,4}
Biruncitruncated 7-orthoplex (Baptize) (0,0,1,1,2,3,3)√2 120960 20160
36 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,3,4{3,3,3,3,3,4}
Steriruncinated 7-orthoplex (Copaz) (0,1,1,1,2,3,3)√2 67200 13440
37 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,3,4{3,3,3,3,3,4}
Biruncicantellated 7-orthoplex (Boparz) (0,0,1,2,2,3,3)√2 100800 20160
38 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2,3,4{4,3,3,3,3,3}
Tricantitruncated 7-cube (Gotrasaz) (0,0,0,1,2,3,3)√2 53760 13440
39 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,5{3,3,3,3,3,4}
Pentitruncated 7-orthoplex (Tetaz) (0,1,1,1,1,2,3)√2 87360 13440
40 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,5{3,3,3,3,3,4}
Penticantellated 7-orthoplex (Teroz) (0,1,1,1,2,2,3)√2 188160 26880
41 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,5{3,3,3,3,3,4}
Bisteritruncated 7-orthoplex (Boctaz) (0,1,1,1,2,3,3)√2 147840 26880
42 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,3,5{3,3,3,3,3,4}
Pentiruncinated 7-orthoplex (Topaz) (0,1,1,2,2,2,3)√2 174720 26880
43 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,3,5{4,3,3,3,3,3}
Bistericantellated 7-cube (Bacresaz) (0,1,1,2,2,3,3)√2 241920 40320
44 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,3,4{4,3,3,3,3,3}
Biruncicantellated 7-cube (Bopresa) (0,1,1,2,3,3,3)√2 120960 26880
45 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,4,5{3,3,3,3,3,4}
Pentistericated 7-orthoplex (Tocaz) (0,1,2,2,2,2,3)√2 67200 13440
46 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,5{4,3,3,3,3,3}
Bisteritruncated 7-cube (Bactasa) (0,1,2,2,2,3,3)√2 147840 26880
47 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,2,4{4,3,3,3,3,3}
Biruncitruncated 7-cube (Biptesa) (0,1,2,2,3,3,3)√2 134400 26880
48 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,2,3{4,3,3,3,3,3}
Bicantitruncated 7-cube (Gibrosa) (0,1,2,3,3,3,3)√2 47040 13440
49 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,6{3,3,3,3,3,4}
Hexitruncated 7-orthoplex (Putaz) (0,0,0,0,0,1,2)√2 + (1,1,1,1,1,1,1) 29568 5376
50 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,6{3,3,3,3,3,4}
Hexicantellated 7-orthoplex (Puraz) (0,0,0,0,1,1,2)√2 + (1,1,1,1,1,1,1) 94080 13440
51 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,4,5{4,3,3,3,3,3}
Pentistericated 7-cube (Tacosa) (0,0,0,0,1,2,2)√2 + (1,1,1,1,1,1,1) 67200 13440
52 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,3,6{4,3,3,3,3,3}
Hexiruncinated 7-cube (Pupsez) (0,0,0,1,1,1,2)√2 + (1,1,1,1,1,1,1) 134400 17920
53 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,3,5{4,3,3,3,3,3}
Pentiruncinated 7-cube (Tapsa) (0,0,0,1,1,2,2)√2 + (1,1,1,1,1,1,1) 174720 26880
54 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,3,4{4,3,3,3,3,3}
Steriruncinated 7-cube (Capsa) (0,0,0,1,2,2,2)√2 + (1,1,1,1,1,1,1) 80640 17920
55 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,6{4,3,3,3,3,3}
Hexicantellated 7-cube (Purosa) (0,0,1,1,1,1,2)√2 + (1,1,1,1,1,1,1) 94080 13440
56 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,2,5{4,3,3,3,3,3}
Penticantellated 7-cube (Tersa) (0,0,1,1,1,2,2)√2 + (1,1,1,1,1,1,1) 188160 26880
57 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,2,4{4,3,3,3,3,3}
Stericantellated 7-cube (Carsa) (0,0,1,1,2,2,2)√2 + (1,1,1,1,1,1,1) 161280 26880
58 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,2,3{4,3,3,3,3,3}
Runcicantellated 7-cube (Parsa) (0,0,1,2,2,2,2)√2 + (1,1,1,1,1,1,1) 53760 13440
59 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,6{4,3,3,3,3,3}
Hexitruncated 7-cube (Putsa) (0,1,1,1,1,1,2)√2 + (1,1,1,1,1,1,1) 29568 5376
60 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,5{4,3,3,3,3,3}
Pentitruncated 7-cube (Tetsa) (0,1,1,1,1,2,2)√2 + (1,1,1,1,1,1,1) 87360 13440
61 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,4{4,3,3,3,3,3}
Steritruncated 7-cube (Catsa) (0,1,1,1,2,2,2)√2 + (1,1,1,1,1,1,1) 116480 17920
62 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,3{4,3,3,3,3,3}
Runcitruncated 7-cube (Petsa) (0,1,1,2,2,2,2)√2 + (1,1,1,1,1,1,1) 73920 13440
63 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,2{4,3,3,3,3,3}
Cantitruncated 7-cube (Gersa) (0,1,2,2,2,2,2)√2 + (1,1,1,1,1,1,1) 18816 5376
64 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3{3,3,3,3,3,4}
Runcicantitruncated 7-orthoplex (Gopaz) (0,1,2,3,4,4,4)√2 60480 13440
65 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,4{3,3,3,3,3,4}
Stericantitruncated 7-orthoplex (Cogarz) (0,0,1,1,2,3,4)√2 241920 40320
66 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3,4{3,3,3,3,3,4}
Steriruncitruncated 7-orthoplex (Captaz) (0,0,1,2,2,3,4)√2 181440 40320
67 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,3,4{3,3,3,3,3,4}
Steriruncicantellated 7-orthoplex (Caparz) (0,0,1,2,3,3,4)√2 181440 40320
68 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,3,4{3,3,3,3,3,4}
Biruncicantitruncated 7-orthoplex (Gibpaz) (0,0,1,2,3,4,4)√2 161280 40320
69 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,5{3,3,3,3,3,4}
Penticantitruncated 7-orthoplex (Tograz) (0,1,1,1,2,3,4)√2 295680 53760
70 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3,5{3,3,3,3,3,4}
Pentiruncitruncated 7-orthoplex (Toptaz) (0,1,1,2,2,3,4)√2 443520 80640
71 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,3,5{3,3,3,3,3,4}
Pentiruncicantellated 7-orthoplex (Toparz) (0,1,1,2,3,3,4)√2 403200 80640
72 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,3,5{3,3,3,3,3,4}
Bistericantitruncated 7-orthoplex (Becogarz) (0,1,1,2,3,4,4)√2 362880 80640
73 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,4,5{3,3,3,3,3,4}
Pentisteritruncated 7-orthoplex (Tacotaz) (0,1,2,2,2,3,4)√2 241920 53760
74 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,4,5{3,3,3,3,3,4}
Pentistericantellated 7-orthoplex (Tocarz) (0,1,2,2,3,3,4)√2 403200 80640
75 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,4,5{4,3,3,3,3,3}
Bisteriruncitruncated 7-cube (Bocaptosaz) (0,1,2,2,3,4,4)√2 322560 80640
76 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,3,4,5{3,3,3,3,3,4}
Pentisteriruncinated 7-orthoplex (Tecpaz) (0,1,2,3,3,3,4)√2 241920 53760
77 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,3,5{4,3,3,3,3,3}
Bistericantitruncated 7-cube (Becgresa) (0,1,2,3,3,4,4)√2 362880 80640
78 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,2,3,4{4,3,3,3,3,3}
Biruncicantitruncated 7-cube (Gibposa) (0,1,2,3,4,4,4)√2 188160 53760
79 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,6{3,3,3,3,3,4}
Hexicantitruncated 7-orthoplex (Pugarez) (0,0,0,0,1,2,3)√2 + (1,1,1,1,1,1,1) 134400 26880
80 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3,6{3,3,3,3,3,4}
Hexiruncitruncated 7-orthoplex (Papataz) (0,0,0,1,1,2,3)√2 + (1,1,1,1,1,1,1) 322560 53760
81 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,3,6{3,3,3,3,3,4}
Hexiruncicantellated 7-orthoplex (Puparez) (0,0,0,1,2,2,3)√2 + (1,1,1,1,1,1,1) 268800 53760
82 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,3,4,5{4,3,3,3,3,3}
Pentisteriruncinated 7-cube (Tecpasa) (0,0,0,1,2,3,3)√2 + (1,1,1,1,1,1,1) 241920 53760
83 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,4,6{3,3,3,3,3,4}
Hexisteritruncated 7-orthoplex (Pucotaz) (0,0,1,1,1,2,3)√2 + (1,1,1,1,1,1,1) 322560 53760
84 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,4,6{4,3,3,3,3,3}
Hexistericantellated 7-cube (Pucrosaz) (0,0,1,1,2,2,3)√2 + (1,1,1,1,1,1,1) 483840 80640
85 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,2,4,5{4,3,3,3,3,3}
Pentistericantellated 7-cube (Tecresa) (0,0,1,1,2,3,3)√2 + (1,1,1,1,1,1,1) 403200 80640
86 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,3,6{4,3,3,3,3,3}
Hexiruncicantellated 7-cube (Pupresa) (0,0,1,2,2,2,3)√2 + (1,1,1,1,1,1,1) 268800 53760
87 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,2,3,5{4,3,3,3,3,3}
Pentiruncicantellated 7-cube (Topresa) (0,0,1,2,2,3,3)√2 + (1,1,1,1,1,1,1) 403200 80640
88 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,2,3,4{4,3,3,3,3,3}
Steriruncicantellated 7-cube (Copresa) (0,0,1,2,3,3,3)√2 + (1,1,1,1,1,1,1) 215040 53760
89 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,5,6{4,3,3,3,3,3}
Hexipentitruncated 7-cube (Putatosez) (0,1,1,1,1,2,3)√2 + (1,1,1,1,1,1,1) 134400 26880
90 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,4,6{4,3,3,3,3,3}
Hexisteritruncated 7-cube (Pacutsa) (0,1,1,1,2,2,3)√2 + (1,1,1,1,1,1,1) 322560 53760
91 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,4,5{4,3,3,3,3,3}
Pentisteritruncated 7-cube (Tecatsa) (0,1,1,1,2,3,3)√2 + (1,1,1,1,1,1,1) 241920 53760
92 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,3,6{4,3,3,3,3,3}
Hexiruncitruncated 7-cube (Pupetsa) (0,1,1,2,2,2,3)√2 + (1,1,1,1,1,1,1) 322560 53760
93 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,3,5{4,3,3,3,3,3}
Pentiruncitruncated 7-cube (Toptosa) (0,1,1,2,2,3,3)√2 + (1,1,1,1,1,1,1) 443520 80640
94 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,3,4{4,3,3,3,3,3}
Steriruncitruncated 7-cube (Captesa) (0,1,1,2,3,3,3)√2 + (1,1,1,1,1,1,1) 215040 53760
95 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,2,6{4,3,3,3,3,3}
Hexicantitruncated 7-cube (Pugrosa) (0,1,2,2,2,2,3)√2 + (1,1,1,1,1,1,1) 134400 26880
96 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,2,5{4,3,3,3,3,3}
Penticantitruncated 7-cube (Togresa) (0,1,2,2,2,3,3)√2 + (1,1,1,1,1,1,1) 295680 53760
97 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,2,4{4,3,3,3,3,3}
Stericantitruncated 7-cube (Cogarsa) (0,1,2,2,3,3,3)√2 + (1,1,1,1,1,1,1) 268800 53760
98 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,2,3{4,3,3,3,3,3}
Runcicantitruncated 7-cube (Gapsa) (0,1,2,3,3,3,3)√2 + (1,1,1,1,1,1,1) 94080 26880
99 CDel node.pngCDel 4.pngCDel node.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
t0,1,2,3,4{3,3,3,3,3,4}
Steriruncicantitruncated 7-orthoplex (Gocaz) (0,0,1,2,3,4,5)√2 322560 80640
100 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3,5{3,3,3,3,3,4}
Pentiruncicantitruncated 7-orthoplex (Tegopaz) (0,1,1,2,3,4,5)√2 725760 161280
101 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,4,5{3,3,3,3,3,4}
Pentistericantitruncated 7-orthoplex (Tecagraz) (0,1,2,2,3,4,5)√2 645120 161280
102 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3,4,5{3,3,3,3,3,4}
Pentisteriruncitruncated 7-orthoplex (Tecpotaz) (0,1,2,3,3,4,5)√2 645120 161280
103 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,3,4,5{3,3,3,3,3,4}
Pentisteriruncicantellated 7-orthoplex (Tacparez) (0,1,2,3,4,4,5)√2 645120 161280
104 CDel node.pngCDel 4.pngCDel 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.png
t1,2,3,4,5{4,3,3,3,3,3}
Bisteriruncicantitruncated 7-cube (Gabcosaz) (0,1,2,3,4,5,5)√2 564480 161280
105 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3,6{3,3,3,3,3,4}
Hexiruncicantitruncated 7-orthoplex (Pugopaz) (0,0,0,1,2,3,4)√2 + (1,1,1,1,1,1,1) 483840 107520
106 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,4,6{3,3,3,3,3,4}
Hexistericantitruncated 7-orthoplex (Pucagraz) (0,0,1,1,2,3,4)√2 + (1,1,1,1,1,1,1) 806400 161280
107 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3,4,6{3,3,3,3,3,4}
Hexisteriruncitruncated 7-orthoplex (Pucpotaz) (0,0,1,2,2,3,4)√2 + (1,1,1,1,1,1,1) 725760 161280
108 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,3,4,6{4,3,3,3,3,3}
Hexisteriruncicantellated 7-cube (Pucprosaz) (0,0,1,2,3,3,4)√2 + (1,1,1,1,1,1,1) 725760 161280
109 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,2,3,4,5{4,3,3,3,3,3}
Pentisteriruncicantellated 7-cube (Tocpresa) (0,0,1,2,3,4,4)√2 + (1,1,1,1,1,1,1) 645120 161280
110 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,5,6{3,3,3,3,3,4}
Hexipenticantitruncated 7-orthoplex (Putegraz) (0,1,1,1,2,3,4)√2 + (1,1,1,1,1,1,1) 483840 107520
111 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3,5,6{4,3,3,3,3,3}
Hexipentiruncitruncated 7-cube (Putpetsaz) (0,1,1,2,2,3,4)√2 + (1,1,1,1,1,1,1) 806400 161280
112 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,3,4,6{4,3,3,3,3,3}
Hexisteriruncitruncated 7-cube (Pucpetsa) (0,1,1,2,3,3,4)√2 + (1,1,1,1,1,1,1) 725760 161280
113 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,3,4,5{4,3,3,3,3,3}
Pentisteriruncitruncated 7-cube (Tecpetsa) (0,1,1,2,3,4,4)√2 + (1,1,1,1,1,1,1) 645120 161280
114 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,5,6{4,3,3,3,3,3}
Hexipenticantitruncated 7-cube (Putgresa) (0,1,2,2,2,3,4)√2 + (1,1,1,1,1,1,1) 483840 107520
115 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,2,4,6{4,3,3,3,3,3}
Hexistericantitruncated 7-cube (Pucagrosa) (0,1,2,2,3,3,4)√2 + (1,1,1,1,1,1,1) 806400 161280
116 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,2,4,5{4,3,3,3,3,3}
Pentistericantitruncated 7-cube (Tecgresa) (0,1,2,2,3,4,4)√2 + (1,1,1,1,1,1,1) 645120 161280
117 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,2,3,6{4,3,3,3,3,3}
Hexiruncicantitruncated 7-cube (Pugopsa) (0,1,2,3,3,3,4)√2 + (1,1,1,1,1,1,1) 483840 107520
118 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,2,3,5{4,3,3,3,3,3}
Pentiruncicantitruncated 7-cube (Togapsa) (0,1,2,3,3,4,4)√2 + (1,1,1,1,1,1,1) 725760 161280
119 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,2,3,4{4,3,3,3,3,3}
Steriruncicantitruncated 7-cube (Gacosa) (0,1,2,3,4,4,4)√2 + (1,1,1,1,1,1,1) 376320 107520
120 CDel node.pngCDel 4.pngCDel 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
t0,1,2,3,4,5{3,3,3,3,3,4}
Pentisteriruncicantitruncated 7-orthoplex (Gotaz) (0,1,2,3,4,5,6)√2 1128960 322560
121 CDel node 1.pngCDel 4.pngCDel node.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
t0,1,2,3,4,6{3,3,3,3,3,4}
Hexisteriruncicantitruncated 7-orthoplex (Pugacaz) (0,0,1,2,3,4,5)√2 + (1,1,1,1,1,1,1) 1290240 322560
122 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3,5,6{3,3,3,3,3,4}
Hexipentiruncicantitruncated 7-orthoplex (Putgapaz) (0,1,1,2,3,4,5)√2 + (1,1,1,1,1,1,1) 1290240 322560
123 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,4,5,6{4,3,3,3,3,3}
Hexipentistericantitruncated 7-cube (Putcagrasaz) (0,1,2,2,3,4,5)√2 + (1,1,1,1,1,1,1) 1290240 322560
124 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3,5,6{4,3,3,3,3,3}
Hexipentiruncicantitruncated 7-cube (Putgapsa) (0,1,2,3,3,4,5)√2 + (1,1,1,1,1,1,1) 1290240 322560
125 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,2,3,4,6{4,3,3,3,3,3}
Hexisteriruncicantitruncated 7-cube (Pugacasa) (0,1,2,3,4,4,5)√2 + (1,1,1,1,1,1,1) 1290240 322560
126 CDel node 1.pngCDel 4.pngCDel 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.png
t0,1,2,3,4,5{4,3,3,3,3,3}
Pentisteriruncicantitruncated 7-cube (Gotesa) (0,1,2,3,4,5,5)√2 + (1,1,1,1,1,1,1) 1128960 322560
127 CDel node 1.pngCDel 4.pngCDel 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
t0,1,2,3,4,5,6{4,3,3,3,3,3}
Omnitruncated 7-cube (Guposaz) (0,1,2,3,4,5,6)√2 + (1,1,1,1,1,1,1) 2257920 645120

The D7 family[edit]

The D7 family has symmetry of order 322560 (7 factorial x 26).

This family has 3×32−1=95 Wythoffian uniform polytopes, generated by marking one or more nodes of the D7 Coxeter-Dynkin diagram. Of these, 63 (2×32−1) are repeated from the B7 family and 32 are unique to this family, listed below. Bowers names and acronym are given for cross-referencing.

See also list of D7 polytopes for Coxeter plane graphs of these polytopes.

# Coxeter diagram Names Base point
(Alternately signed)
Element counts
6 5 4 3 2 1 0
1 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h1.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 7-demicube
Demihepteract (Hesa)
(1,1,1,1,1,1,1) 78 532 1624 2800 2240 672 64
2 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png Truncated 7-demicube
Truncated demihepteract (Thesa)
(1,1,3,3,3,3,3) 142 1428 5656 11760 13440 7392 1344
3 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png Cantellated 7-demicube
Small rhombated demihepteract (Sirhesa)
(1,1,1,3,3,3,3) 16800 2240
4 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png Runcinated 7-demicube
Small prismated demihepteract (Sphosa)
(1,1,1,1,3,3,3) 20160 2240
5 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png Stericated 7-demicube
Small cellated demihepteract (Sochesa)
(1,1,1,1,1,3,3) 13440 1344
6 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png Pentellated 7-demicube
Small terated demihepteract (Suthesa)
(1,1,1,1,1,1,3) 4704 448
7 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png Cantitruncated 7-demicube
Great rhombated demihepteract (Girhesa)
(1,1,3,5,5,5,5) 23520 6720
8 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png Runcitruncated 7-demicube
Prismatotruncated demihepteract (Pothesa)
(1,1,3,3,5,5,5) 73920 13440
9 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png Runcicantellated 7-demicube
Prismatorhomated demihepteract (Prohesa)
(1,1,1,3,5,5,5) 40320 8960
10 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png Steritruncated 7-demicube
Cellitruncated demihepteract (Cothesa)
(1,1,3,3,3,5,5) 87360 13440
11 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png Stericantellated 7-demicube
Cellirhombated demihepteract (Crohesa)
(1,1,1,3,3,5,5) 87360 13440
12 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png Steriruncinated 7-demicube
Celliprismated demihepteract (Caphesa)
(1,1,1,1,3,5,5) 40320 6720
13 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png Pentitruncated 7-demicube
Teritruncated demihepteract (Tuthesa)
(1,1,3,3,3,3,5) 43680 6720
14 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png Penticantellated 7-demicube
Terirhombated demihepteract (Turhesa)
(1,1,1,3,3,3,5) 67200 8960
15 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png Pentiruncinated 7-demicube
Teriprismated demihepteract (Tuphesa)
(1,1,1,1,3,3,5) 53760 6720
16 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png Pentistericated 7-demicube
Tericellated demihepteract (Tuchesa)
(1,1,1,1,1,3,5) 21504 2688
17 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png Runcicantitruncated 7-demicube
Great prismated demihepteract (Gephosa)
(1,1,3,5,7,7,7) 94080 26880
18 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png Stericantitruncated 7-demicube
Celligreatorhombated demihepteract (Cagrohesa)
(1,1,3,5,5,7,7) 181440 40320
19 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png Steriruncitruncated 7-demicube
Celliprismatotruncated demihepteract (Capthesa)
(1,1,3,3,5,7,7) 181440 40320
20 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png Steriruncicantellated 7-demicube
Celliprismatorhombated demihepteract (Coprahesa)
(1,1,1,3,5,7,7) 120960 26880
21 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png Penticantitruncated 7-demicube
Terigreatorhombated demihepteract (Tugrohesa)
(1,1,3,5,5,5,7) 120960 26880
22 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png Pentiruncitruncated 7-demicube
Teriprismatotruncated demihepteract (Tupthesa)
(1,1,3,3,5,5,7) 221760 40320
23 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png Pentiruncicantellated 7-demicube
Teriprismatorhombated demihepteract (Tuprohesa)
(1,1,1,3,5,5,7) 134400 26880
24 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png Pentisteritruncated 7-demicube
Tericellitruncated demihepteract (Tucothesa)
(1,1,3,3,3,5,7) 147840 26880
25 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png Pentistericantellated 7-demicube
Tericellirhombated demihepteract (Tucrohesa)
(1,1,1,3,3,5,7) 161280 26880
26 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png Pentisteriruncinated 7-demicube
Tericelliprismated demihepteract (Tucophesa)
(1,1,1,1,3,5,7) 80640 13440
27 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png Steriruncicantitruncated 7-demicube
Great cellated demihepteract (Gochesa)
(1,1,3,5,7,9,9) 282240 80640
28 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png Pentiruncicantitruncated 7-demicube
Terigreatoprimated demihepteract (Tugphesa)
(1,1,3,5,7,7,9) 322560 80640
29 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png Pentistericantitruncated 7-demicube
Tericelligreatorhombated demihepteract (Tucagrohesa)
(1,1,3,5,5,7,9) 322560 80640
30 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png Pentisteriruncitruncated 7-demicube
Tericelliprismatotruncated demihepteract (Tucpathesa)
(1,1,3,3,5,7,9) 362880 80640
31 CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png Pentisteriruncicantellated 7-demicube
Tericellprismatorhombated demihepteract (Tucprohesa)
(1,1,1,3,5,7,9) 241920 53760
32 CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h1.pngCDel 4.pngCDel node.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 Pentisteriruncicantitruncated 7-demicube
Great terated demihepteract (Guthesa)
(1,1,3,5,7,9,11) 564480 161280

The E7 family[edit]

The E7 Coxeter group has order 2,903,040.

There are 127 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings.

See also a list of E7 polytopes for symmetric Coxeter plane graphs of these polytopes.

# Coxeter-Dynkin diagram
Schläfli symbol
Names Element counts
6 5 4 3 2 1 0
1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png 231 (laq) 632 4788 16128 20160 10080 2016 126
2 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png Rectified 231 (rolaq) 758 10332 47880 100800 90720 30240 2016
3 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png Rectified 132 (rolin) 758 12348 72072 191520 241920 120960 10080
4 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 132 (lin) 182 4284 23688 50400 40320 10080 576
5 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png Birectified 321 (branq) 758 12348 68040 161280 161280 60480 4032
6 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png Rectified 321 (ranq) 758 44352 70560 48384 11592 12096 756
7 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png 321 (naq) 702 6048 12096 10080 4032 756 56
8 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png Truncated 231 (talq) 758 10332 47880 100800 90720 32256 4032
9 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png Cantellated 231 (sirlaq) 131040 20160
10 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png Bitruncated 231 (botlaq) 30240
11 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png small demified 231 (shilq) 2774 22428 78120 151200 131040 42336 4032
12 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png demirectified 231 (hirlaq) 12096
13 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png truncated 132 (tolin) 20160
14 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png small demiprismated 231 (shiplaq) 20160
15 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png birectified 132 (berlin) 758 22428 142632 403200 544320 302400 40320
16 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png tritruncated 321 (totanq) 40320
17 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png demibirectified 321 (hobranq) 20160
18 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png small cellated 231 (scalq) 7560
19 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png small biprismated 231 (sobpalq) 30240
20 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png small birhombated 321 (sabranq) 60480
21 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png demirectified 321 (harnaq) 12096
22 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png bitruncated 321 (botnaq) 12096
23 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png small terated 321 (stanq) 1512
24 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png small demicellated 321 (shocanq) 12096
25 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png small prismated 321 (spanq) 40320
26 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png small demified 321 (shanq) 4032
27 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png small rhombated 321 (sranq) 12096
28 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png Truncated 321 (tanq) 758 11592 48384 70560 44352 12852 1512
29 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png great rhombated 231 (girlaq) 60480
30 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png demitruncated 231 (hotlaq) 24192
31 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png small demirhombated 231 (sherlaq) 60480
32 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png demibitruncated 231 (hobtalq) 60480
33 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png demiprismated 231 (hiptalq) 80640
34 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png demiprismatorhombated 231 (hiprolaq) 120960
35 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png bitruncated 132 (batlin) 120960
36 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png small prismated 231 (spalq) 80640
37 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png small rhombated 132 (sirlin) 120960
38 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png tritruncated 231 (tatilq) 80640
39 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png cellitruncated 231 (catalaq) 60480
40 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png cellirhombated 231 (crilq) 362880
41 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png biprismatotruncated 231 (biptalq) 181440
42 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png small prismated 132 (seplin) 60480
43 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png small biprismated 321 (sabipnaq) 120960
44 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png small demibirhombated 321 (shobranq) 120960
45 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png cellidemiprismated 231 (chaplaq) 60480
46 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png demibiprismatotruncated 321 (hobpotanq) 120960
47 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png great birhombated 321 (gobranq) 120960
48 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png demibitruncated 321 (hobtanq) 60480
49 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png teritruncated 231 (totalq) 24192
50 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png terirhombated 231 (trilq) 120960
51 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png demicelliprismated 321 (hicpanq) 120960
52 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png small teridemified 231 (sethalq) 24192
53 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png small cellated 321 (scanq) 60480
54 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png demiprismated 321 (hipnaq) 80640
55 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png terirhombated 321 (tranq) 60480
56 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png demicellirhombated 321 (hocranq) 120960
57 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png prismatorhombated 321 (pranq) 120960
58 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png small demirhombated 321 (sharnaq) 60480
59 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png teritruncated 321 (tetanq) 15120
60 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png demicellitruncated 321 (hictanq) 60480
61 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png prismatotruncated 321 (potanq) 120960
62 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png demitruncated 321 (hotnaq) 24192
63 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png great rhombated 321 (granq) 24192
64 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png great demified 231 (gahlaq) 120960
65 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png great demiprismated 231 (gahplaq) 241920
66 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png prismatotruncated 231 (potlaq) 241920
67 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png prismatorhombated 231 (prolaq) 241920
68 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png great rhombated 132 (girlin) 241920
69 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png celligreatorhombated 231 (cagrilq) 362880
70 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png cellidemitruncated 231 (chotalq) 241920
71 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png prismatotruncated 132 (patlin) 362880
72 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png biprismatorhombated 321 (bipirnaq) 362880
73 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png tritruncated 132 (tatlin) 241920
74 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png cellidemiprismatorhombated 231 (chopralq) 362880
75 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png great demibiprismated 321 (ghobipnaq) 362880
76 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png celliprismated 231 (caplaq) 241920
77 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png biprismatotruncated 321 (boptanq) 362880
78 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png great trirhombated 231 (gatralaq) 241920
79 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png terigreatorhombated 231 (togrilq) 241920
80 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png teridemitruncated 231 (thotalq) 120960
81 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png teridemirhombated 231 (thorlaq) 241920
82 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png celliprismated 321 (capnaq) 241920
83 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png teridemiprismatotruncated 231 (thoptalq) 241920
84 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png teriprismatorhombated 321 (tapronaq) 362880
85 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png demicelliprismatorhombated 321 (hacpranq) 362880
86 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png teriprismated 231 (toplaq) 241920
87 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png cellirhombated 321 (cranq) 362880
88 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png demiprismatorhombated 321 (hapranq) 241920
89 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png tericellitruncated 231 (tectalq) 120960
90 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png teriprismatotruncated 321 (toptanq) 362880
91 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png demicelliprismatotruncated 321 (hecpotanq) 362880
92 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png teridemitruncated 321 (thotanq) 120960
93 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png cellitruncated 321 (catnaq) 241920
94 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png demiprismatotruncated 321 (hiptanq) 241920
95 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png terigreatorhombated 321 (tagranq) 120960
96 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png demicelligreatorhombated 321 (hicgarnq) 241920
97 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png great prismated 321 (gopanq) 241920
98 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png great demirhombated 321 (gahranq) 120960
99 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png great prismated 231 (gopalq) 483840
100 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png great cellidemified 231 (gechalq) 725760
101 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png great birhombated 132 (gebrolin) 725760
102 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png prismatorhombated 132 (prolin) 725760
103 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png celliprismatorhombated 231 (caprolaq) 725760
104 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png great biprismated 231 (gobpalq) 725760
105 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png tericelliprismated 321 (ticpanq) 483840
106 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png teridemigreatoprismated 231 (thegpalq) 725760
107 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png teriprismatotruncated 231 (teptalq) 725760
108 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png teriprismatorhombated 231 (topralq) 725760
109 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png cellipriemsatorhombated 321 (copranq) 725760
110 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png tericelligreatorhombated 231 (tecgrolaq) 725760
111 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png tericellitruncated 321 (tectanq) 483840
112 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png teridemiprismatotruncated 321 (thoptanq) 725760
113 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png celliprismatotruncated 321 (coptanq) 725760
114 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png teridemicelligreatorhombated 321 (thocgranq) 483840
115 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png terigreatoprismated 321 (tagpanq) 725760
116 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png great demicellated 321 (gahcnaq) 725760
117 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png tericelliprismated laq (tecpalq) 483840
118 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png celligreatorhombated 321 (cogranq) 725760
119 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png great demified 321 (gahnq) 483840
120 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png great cellated 231 (gocalq) 1451520
121 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png terigreatoprismated 231 (tegpalq) 1451520
122 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png tericelliprismatotruncated 321 (tecpotniq) 1451520
123 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 10.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png tericellidemigreatoprismated 231 (techogaplaq) 1451520
124 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 01lr.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png tericelligreatorhombated 321 (tacgarnq) 1451520
125 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png tericelliprismatorhombated 231 (tecprolaq) 1451520
126 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png great cellated 321 (gocanq) 1451520
127 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel branch 11.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png great terated 321 (gotanq) 2903040

Regular and uniform honeycombs[edit]

Coxeter-Dynkin diagram correspondences between families and higher symmetry within diagrams. Nodes of the same color in each row represent identical mirrors. Black nodes are not active in the correspondence.

There are five fundamental affine Coxeter groups and sixteen prismatic groups that generate regular and uniform tessellations in 6-space:

# Coxeter group Coxeter diagram Forms
1 {\tilde{A}}_6 [3[7]] CDel branch.pngCDel 3ab.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel split2.png