Pentellated 7-simplexes

From Wikipedia, the free encyclopedia
  (Redirected from Pentellated 7-simplex)
Jump to: navigation, search
7-simplex t0.svg
7-simplex
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.png
7-simplex t05.svg
Pentellated 7-simplex
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.png
7-simplex t015.svg
Pentitruncated 7-simplex
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.png
7-simplex t025.svg
Penticantellated 7-simplex
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.png
7-simplex t0125.svg
Penticantitruncated 7-simplex
CDel 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.pngCDel 3.pngCDel node.png
7-simplex t035.svg
Pentiruncinated 7-simplex
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.png
7-simplex t0135.svg
Pentiruncitruncated 7-simplex
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.png
7-simplex t0235.svg
Pentiruncicantellated 7-simplex
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.png
7-simplex t01235.svg
Pentiruncicantitruncated 7-simplex
CDel 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.pngCDel 3.pngCDel node.png
7-simplex t045.svg
Pentistericated 7-simplex
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.png
7-simplex t0145.svg
Pentisteritruncated 7-simplex
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.png
7-simplex t0245.svg
Pentistericantellated 7-simplex
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.png
7-simplex t01245.svg
Pentistericantitruncated 7-simplex
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.png
7-simplex t0345.svg
Pentisteriruncinated 7-simplex
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.png
7-simplex t01345.svg
Pentisteriruncitruncated 7-simplex
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.png
7-simplex t02345.svg
Pentisteriruncicantellated 7-simplex
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.png
7-simplex t012345.svg
Pentisteriruncicantitruncated 7-simplex
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.png

In seven-dimensional geometry, a pentellated 7-simplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-simplex.

There are 16 unique pentellations of the 7-simplex with permutations of truncations, cantellations, runcinations, and sterications.

Pentellated 7-simplex[edit]

Pentellated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 1260
Vertices 168
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Small terated octaexon (acronym: seto) (Jonathan Bowers)[1]

Coordinates[edit]

The vertices of the pentellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,1,1,2). This construction is based on facets of the pentellated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t05.svg 7-simplex t05 A6.svg 7-simplex t05 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t05 A4.svg 7-simplex t05 A3.svg 7-simplex t05 A2.svg
Dihedral symmetry [5] [4] [3]

Pentitruncated 7-simplex[edit]

pentitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 5460
Vertices 840
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Teritruncated octaexon (acronym: teto) (Jonathan Bowers)[2]

Coordinates[edit]

The vertices of the pentitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,1,2,3). This construction is based on facets of the pentitruncated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t015.svg 7-simplex t015 A6.svg 7-simplex t015 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t015 A4.svg 7-simplex t015 A3.svg 7-simplex t015 A2.svg
Dihedral symmetry [5] [4] [3]

Penticantellated 7-simplex[edit]

Penticantellated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,2,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 11760
Vertices 1680
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Terirhombated octaexon (acronym: tero) (Jonathan Bowers)[3]

Coordinates[edit]

The vertices of the penticantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,2,2,3). This construction is based on facets of the penticantellated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t025.svg 7-simplex t025 A6.svg 7-simplex t025 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t025 A4.svg 7-simplex t025 A3.svg 7-simplex t025 A2.svg
Dihedral symmetry [5] [4] [3]

Penticantitruncated 7-simplex[edit]

penticantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams CDel 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.pngCDel 3.pngCDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Terigreatorhombated octaexon (acronym: tegro) (Jonathan Bowers)[4]

Coordinates[edit]

The vertices of the penticantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,1,2,3,4). This construction is based on facets of the penticantitruncated 8-orthoplex.

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t125.svg 7-simplex t125 A6.svg 7-simplex t125 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t125 A4.svg 7-simplex t125 A3.svg 7-simplex t125 A2.svg
Dihedral symmetry [5] [4] [3]

Pentiruncinated 7-simplex[edit]

pentiruncinated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,3,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 10920
Vertices 1680
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Teriprismated octaexon (acronym: tepo) (Jonathan Bowers)[5]

Coordinates[edit]

The vertices of the pentiruncinated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,2,2,3). This construction is based on facets of the pentiruncinated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t135.svg 7-simplex t135 A6.svg 7-simplex t135 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t135 A4.svg 7-simplex t135 A3.svg 7-simplex t135 A2.svg
Dihedral symmetry [5] [4] [3]

Pentiruncitruncated 7-simplex[edit]

pentiruncitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,3,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 27720
Vertices 5040
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Teriprismatotruncated octaexon (acronym: tapto) (Jonathan Bowers)[6]

Coordinates[edit]

The vertices of the pentiruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,2,3,4). This construction is based on facets of the pentiruncitruncated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t0135.svg 7-simplex t0135 A6.svg 7-simplex t0135 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t0135 A4.svg 7-simplex t0135 A3.svg 7-simplex t0135 A2.svg
Dihedral symmetry [5] [4] [3]

Pentiruncicantellated 7-simplex[edit]

pentiruncicantellated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,2,3,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 25200
Vertices 5040
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Teriprismatorhombated octaexon (acronym: tapro) (Jonathan Bowers)[7]

Coordinates[edit]

The vertices of the pentiruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,3,3,4). This construction is based on facets of the pentiruncicantellated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t0235.svg 7-simplex t0235 A6.svg 7-simplex t0235 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t0235 A4.svg 7-simplex t0235 A3.svg 7-simplex t0235 A2.svg
Dihedral symmetry [5] [4] [3]

Pentiruncicantitruncated 7-simplex[edit]

pentiruncicantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams CDel 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.pngCDel 3.pngCDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 45360
Vertices 10080
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Terigreatoprismated octaexon (acronym: tegapo) (Jonathan Bowers)[8]

Coordinates[edit]

The vertices of the pentiruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,3,4,5). This construction is based on facets of the pentiruncicantitruncated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t01235.svg 7-simplex t01235 A6.svg 7-simplex t01235 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t01235 A4.svg 7-simplex t01235 A3.svg 7-simplex t01235 A2.svg
Dihedral symmetry [5] [4] [3]

Pentistericated 7-simplex[edit]

pentistericated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,4,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 4200
Vertices 840
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Tericellated octaexon (acronym: teco) (Jonathan Bowers)[9]

Coordinates[edit]

The vertices of the pentistericated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,2,2,2,3). This construction is based on facets of the pentistericated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t045.svg 7-simplex t045 A6.svg 7-simplex t045 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t045 A4.svg 7-simplex t045 A3.svg 7-simplex t045 A2.svg
Dihedral symmetry [5] [4] [3]

Pentisteritruncated 7-simplex[edit]

pentisteritruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,4,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 15120
Vertices 3360
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Tericellitruncated octaexon (acronym: tecto) (Jonathan Bowers)[10]

Coordinates[edit]

The vertices of the pentisteritruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,2,3,4,4). This construction is based on facets of the pentisteritruncated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t0145.svg 7-simplex t0145 A6.svg 7-simplex t0145 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t0145 A4.svg 7-simplex t0145 A3.svg 7-simplex t0145 A2.svg
Dihedral symmetry [5] [4] [3]

Pentistericantellated 7-simplex[edit]

pentistericantellated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,2,4,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 25200
Vertices 5040
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Tericellirhombated octaexon (acronym: tecro) (Jonathan Bowers)[11]

Coordinates[edit]

The vertices of the pentistericantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,2,3,3,4). This construction is based on facets of the pentistericantellated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t0245.svg 7-simplex t0245 A6.svg 7-simplex t0245 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t0245 A4.svg 7-simplex t0245 A3.svg 7-simplex t0245 A2.svg
Dihedral symmetry [5] [4] [3]

Pentistericantitruncated 7-simplex[edit]

pentistericantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,4,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 40320
Vertices 10080
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Tericelligreatorhombated octaexon (acronym: tecagro) (Jonathan Bowers)[12]

Coordinates[edit]

The vertices of the pentistericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,2,3,4,5). This construction is based on facets of the pentistericantitruncated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t01245.svg 7-simplex t01245 A6.svg 7-simplex t01245 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t01245 A4.svg 7-simplex t01245 A3.svg 7-simplex t01245 A2.svg
Dihedral symmetry [5] [4] [3]

Pentisteriruncinated 7-simplex[edit]

Pentisteriruncinated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,3,4,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 15120
Vertices 3360
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Bipenticantitruncated 7-simplex as t1,2,3,6{3,3,3,3,3,3}
  • Tericelliprismated octaexon (acronym: tacpo) (Jonathan Bowers)[13]

Coordinates[edit]

The vertices of the pentisteriruncinated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,3,3,4). This construction is based on facets of the pentisteriruncinated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t0345.svg 7-simplex t0345 A6.svg 7-simplex t0345 A5.svg
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t0345 A4.svg 7-simplex t0345 A3.svg 7-simplex t0345 A2.svg
Dihedral symmetry [5] [4] [3]

Pentisteriruncitruncated 7-simplex[edit]

pentisteriruncitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,3,4,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 40320
Vertices 10080
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Tericelliprismatotruncated octaexon (acronym: tacpeto) (Jonathan Bowers)[14]

Coordinates[edit]

The vertices of the pentisteriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,3,4,5). This construction is based on facets of the pentisteriruncitruncated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t01345.svg 7-simplex t01345 A6.svg 7-simplex t01345 A5.svg
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t01345 A4.svg 7-simplex t01345 A3.svg 7-simplex t01345 A2.svg
Dihedral symmetry [[5]] [4] [[3]]

Pentisteriruncicantellated 7-simplex[edit]

pentisteriruncicantellated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,2,3,4,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 40320
Vertices 10080
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Bipentiruncicantitruncated 7-simplex as t1,2,3,4,6{3,3,3,3,3,3}
  • Tericelliprismatorhombated octaexon (acronym: tacpro) (Jonathan Bowers)[15]

Coordinates[edit]

The vertices of the pentisteriruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,4,4,5). This construction is based on facets of the pentisteriruncicantellated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t02345.svg 7-simplex t02345 A6.svg 7-simplex t02345 A5.svg
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t02345 A4.svg 7-simplex t02345 A3.svg 7-simplex t02345 A2.svg
Dihedral symmetry [[5]] [4] [[3]]

Pentisteriruncicantitruncated 7-simplex[edit]

pentisteriruncicantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,4,5{3,3,3,3,3,3}
Coxeter-Dynkin diagrams 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.png
6-faces
5-faces
4-faces
Cells
Faces
Edges 70560
Vertices 20160
Vertex figure
Coxeter groups A7, [3,3,3,3,3,3]
Properties convex

Alternate names[edit]

  • Great terated octaexon (acronym: geto) (Jonathan Bowers)[16]

Coordinates[edit]

The vertices of the pentisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,2,3,4,5,6). This construction is based on facets of the pentisteriruncicantitruncated 8-orthoplex.

Images[edit]

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph 7-simplex t012345.svg 7-simplex t012345 A6.svg 7-simplex t012345 A5.svg
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph 7-simplex t012345 A4.svg 7-simplex t012345 A3.svg 7-simplex t012345 A2.svg
Dihedral symmetry [[5]] [4] [[3]]

Related polytopes[edit]

These polytopes are a part of a set of 71 uniform 7-polytopes with A7 symmetry.

Notes[edit]

  1. ^ Klitzing, (x3o3o3o3o3x3o - seto)
  2. ^ Klitzing, (x3x3o3o3o3x3o - teto)
  3. ^ Klitzing, (x3o3x3o3o3x3o - tero)
  4. ^ Klitzing, (x3x3x3oxo3x3o - tegro)
  5. ^ Klitzing, (x3o3o3x3o3x3o - tepo)
  6. ^ Klitzing, (x3x3o3x3o3x3o - tapto)
  7. ^ Klitzing, (x3o3x3x3o3x3o - tapro)
  8. ^ Klitzing, (x3x3x3x3o3x3o - tegapo)
  9. ^ Klitzing, (x3o3o3o3x3x3o - teco)
  10. ^ Klitzing, (x3x3o3o3x3x3o - tecto)
  11. ^ Klitzing, (x3o3x3o3x3x3o - tecro)
  12. ^ Klitzing, (x3x3x3o3x3x3o - tecagro)
  13. ^ Klitzing, (x3o3o3x3x3x3o - tacpo)
  14. ^ Klitzing, (x3x3o3x3x3x3o - tacpeto)
  15. ^ Klitzing, (x3o3x3x3x3x3o - tacpro)
  16. ^ Klitzing, (x3x3x3x3x3x3o - geto)

References[edit]

  • H.S.M. Coxeter:
    • H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
    • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
      • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
      • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
      • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • Norman Johnson Uniform Polytopes, Manuscript (1991)
    • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
  • Klitzing, Richard. "7D uniform polytopes (polyexa)".  x3o3o3o3o3x3o - seto, x3x3o3o3o3x3o - teto, x3o3x3o3o3x3o - tero, x3x3x3oxo3x3o - tegro, x3o3o3x3o3x3o - tepo, x3x3o3x3o3x3o - tapto, x3o3x3x3o3x3o - tapro, x3x3x3x3o3x3o - tegapo, x3o3o3o3x3x3o - teco, x3x3o3o3x3x3o - tecto, x3o3x3o3x3x3o - tecro, x3x3x3o3x3x3o - tecagro, x3o3o3x3x3x3o - tacpo, x3x3o3x3x3x3o - tacpeto, x3o3x3x3x3x3o - tacpro, x3x3x3x3x3x3o - geto

External links[edit]

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / E9 / E10 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron OctahedronCube Demicube DodecahedronIcosahedron
Uniform 4-polytope 5-cell 16-cellTesseract Demitesseract 24-cell 120-cell600-cell
Uniform 5-polytope 5-simplex 5-orthoplex5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex6-cube 6-demicube 122221
Uniform 7-polytope 7-simplex 7-orthoplex7-cube 7-demicube 132231321
Uniform 8-polytope 8-simplex 8-orthoplex8-cube 8-demicube 142241421
Uniform 9-polytope 9-simplex 9-orthoplex9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplexn-cube n-demicube 1k22k1k21 n-pentagonal polytope
Topics: Polytope familiesRegular polytopeList of regular polytopes and compounds