Pentellated 7-cubes

In seven-dimensional geometry, a pentellated 7-cube is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-cube. There are 32 unique pentellations of the 7-cube with permutations of truncations, cantellations, runcinations, and sterications. 16 are more simply constructed relative to the 7-orthoplex.

File:7-cube t0 B6.svg 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t05 B6.svg Pentellated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t015 B6.svg Pentitruncated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t025 B6.svg Penticantellated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
File:7-cube t0125 B6.svg Penticantitruncated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	Pentiruncinated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t0135 B6.svg Pentiruncitruncated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t0235 B6.svg Pentiruncicantellated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
File:7-cube t01235 B6.svg Pentiruncicantitruncated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t045 B6.svg Pentistericated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t0145 B6.svg Pentisteritruncated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t0245 B6.svg Pentistericantellated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
File:7-cube t01245 B6.svg Pentistericantitruncated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t0345 B6.svg Pentisteriruncinated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t01345 B6.svg Pentisteriruncitruncated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png	File:7-cube t02345 B6.svg Pentisteriruncicantellated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
File:7-cube t012345 B6.svg Pentisteriruncicantitruncated 7-cube File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png

Pentellated 7-cube

Pentellated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Small terated hepteract (acronym:) (Jonathan Bowers)^[1]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t05.svg	File:7-cube t05 B6.svg	File:7-cube t05 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t05 B4.svg	File:7-cube t05 B3.svg	File:7-cube t05 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t05 A5.svg	File:7-cube t05 A3.svg
Dihedral symmetry	[6]	[4]

Pentitruncated 7-cube

pentitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,1,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Teritruncated hepteract (acronym: ) (Jonathan Bowers)^[2]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t015.svg	File:7-cube t015 B6.svg	File:7-cube t015 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t015 B4.svg	File:7-cube t015 B3.svg	File:7-cube t015 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t015 A5.svg	File:7-cube t015 A3.svg
Dihedral symmetry	[6]	[4]

Penticantellated 7-cube

Penticantellated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,2,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Terirhombated hepteract (acronym: ) (Jonathan Bowers)^[3]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t025.svg	File:7-cube t025 B6.svg	File:7-cube t025 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t025 B4.svg	File:7-cube t025 B3.svg	File:7-cube t025 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t025 A5.svg	File:7-cube t025 A3.svg
Dihedral symmetry	[6]	[4]

Penticantitruncated 7-cube

penticantitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,1,2,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Terigreatorhombated hepteract (acronym: ) (Jonathan Bowers)^[4]

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t125.svg	File:7-cube t125 B6.svg	File:7-cube t125 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t125 B4.svg	File:7-cube t125 B3.svg	File:7-cube t125 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t125 A5.svg	File:7-cube t125 A3.svg
Dihedral symmetry	[6]	[4]

Pentiruncinated 7-cube

pentiruncinated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,3,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Teriprismated hepteract (acronym: ) (Jonathan Bowers)^[5]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t135.svg	File:7-cube t135 B6.svg	File:7-cube t135 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t135 B4.svg	File:7-cube t135 B3.svg	File:7-cube t135 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t135 A5.svg	File:7-cube t135 A3.svg
Dihedral symmetry	[6]	[4]

Pentiruncitruncated 7-cube

pentiruncitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,1,3,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Teriprismatotruncated hepteract (acronym: ) (Jonathan Bowers)^[6]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t0135.svg	File:7-cube t0135 B6.svg	File:7-cube t0135 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t0135 B4.svg	File:7-cube t0135 B3.svg	File:7-cube t0135 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t0135 A5.svg	File:7-cube t0135 A3.svg
Dihedral symmetry	[6]	[4]

Pentiruncicantellated 7-cube

pentiruncicantellated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,2,3,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Teriprismatorhombated hepteract (acronym: ) (Jonathan Bowers)^[7]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t0235.svg	File:7-cube t0235 B6.svg	File:7-cube t0235 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t0235 B4.svg	File:7-cube t0235 B3.svg	File:7-cube t0235 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t0235 A5.svg	File:7-cube t0235 A3.svg
Dihedral symmetry	[6]	[4]

Pentiruncicantitruncated 7-cube

pentiruncicantitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,1,2,3,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Terigreatoprismated hepteract (acronym: ) (Jonathan Bowers)^[8]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	too complex	File:7-cube t01235 B6.svg	File:7-cube t01235 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t01235 B4.svg	File:7-cube t01235 B3.svg	File:7-cube t01235 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	too complex	too complex
Dihedral symmetry	[6]	[4]

Pentistericated 7-cube

pentistericated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,4,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Tericellated hepteract (acronym: ) (Jonathan Bowers)^[9]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t045.svg	File:7-cube t045 B6.svg	File:7-cube t045 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t045 B4.svg	File:7-cube t045 B3.svg	File:7-cube t045 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t045 A5.svg	File:7-cube t045 A3.svg
Dihedral symmetry	[6]	[4]

Pentisteritruncated 7-cube

pentisteritruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,1,4,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Tericellitruncated hepteract (acronym: ) (Jonathan Bowers)^[10]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t0145.svg	File:7-cube t0145 B6.svg	File:7-cube t0145 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t0145 B4.svg	File:7-cube t0145 B3.svg	File:7-cube t0145 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t0145 A5.svg	File:7-cube t0145 A3.svg
Dihedral symmetry	[6]	[4]

Pentistericantellated 7-cube

pentistericantellated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,2,4,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Tericellirhombated hepteract (acronym: ) (Jonathan Bowers)^[11]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t0245.svg	File:7-cube t0245 B6.svg	File:7-cube t0245 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t0245 B4.svg	File:7-cube t0245 B3.svg	File:7-cube t0245 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t0245 A5.svg	File:7-cube t0245 A3.svg
Dihedral symmetry	[6]	[4]

Pentistericantitruncated 7-cube

pentistericantitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,1,2,4,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Tericelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)^[12]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	too complex	File:7-cube t01245 B6.svg	File:7-cube t01245 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t01245 B4.svg	File:7-cube t01245 B3.svg	File:7-cube t01245 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t01245 A5.svg	File:7-cube t01245 A3.svg
Dihedral symmetry	[6]	[4]

Pentisteriruncinated 7-cube

Pentisteriruncinated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,3,4,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Bipenticantitruncated 7-cube as t_1,2,3,6{4,3⁵}
Tericelliprismated hepteract (acronym: ) (Jonathan Bowers)^[13]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	File:7-cube t0345.svg	File:7-cube t0345 B6.svg	File:7-cube t0345 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t0345 B4.svg	File:7-cube t0345 B3.svg	File:7-cube t0345 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t0345 A5.svg	File:7-cube t0345 A3.svg
Dihedral symmetry	[6]	[4]

Pentisteriruncitruncated 7-cube

pentisteriruncitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,1,3,4,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges	40320
Vertices	10080
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Tericelliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)^[14]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	too complex	File:7-cube t01345 B6.svg	File:7-cube t01345 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t01345 B4.svg	File:7-cube t01345 B3.svg	File:7-cube t01345 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t01345 A5.svg	File:7-cube t01345 A3.svg
Dihedral symmetry	[6]	[4]

Pentisteriruncicantellated 7-cube

pentisteriruncicantellated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,2,3,4,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges	40320
Vertices	10080
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Bipentiruncicantitruncated 7-cube as t_1,2,3,4,6{4,3⁵}
Tericelliprismatorhombated hepteract (acronym: ) (Jonathan Bowers)^[15]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	too complex	File:7-cube t02345 B6.svg	File:7-cube t02345 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t02345 B4.svg	File:7-cube t02345 B3.svg	File:7-cube t02345 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t02345 A5.svg	File:7-cube t02345 A3.svg
Dihedral symmetry	[6]	[4]

Pentisteriruncicantitruncated 7-cube

pentisteriruncicantitruncated 7-cube
Type	uniform 7-polytope
Schläfli symbol	t_0,1,2,3,4,5{4,3⁵}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Alternate names

Great terated hepteract (acronym:) (Jonathan Bowers)^[16]

Images

orthographic projections
Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	too complex	File:7-cube t012345 B6.svg	File:7-cube t012345 B5.svg
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph	File:7-cube t012345 B4.svg	File:7-cube t012345 B3.svg	File:7-cube t012345 B2.svg
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph	File:7-cube t012345 A5.svg	File:7-cube t012345 A3.svg
Dihedral symmetry	[6]	[4]

Related polytopes

These polytopes are a part of a set of 127 uniform 7-polytopes with B₇ symmetry.

Notes

↑ Klitzing, (x3o3o3o3o3x4o - )
↑ Klitzing, (x3x3o3o3o3x4o - )
↑ Klitzing, (x3o3x3o3o3x4o - )
↑ Klitzing, (x3x3x3oxo3x4o - )
↑ Klitzing, (x3o3o3x3o3x4o - )
↑ Klitzing, (x3x3o3x3o3x4o - )
↑ Klitzing, (x3o3x3x3o3x4o - )
↑ Klitzing, (x3x3x3x3o3x4o - )
↑ Klitzing, (x3o3o3o3x3x4o - )
↑ Klitzing, (x3x3o3o3x3x4o - )
↑ Klitzing, (x3o3x3o3x3x4o - )
↑ Klitzing, (x3x3x3o3x3x4o - )
↑ Klitzing, (x3o3o3x3x3x4o - )
↑ Klitzing, (x3x3o3x3x3x4o - )
↑ Klitzing, (x3o3x3x3x3x4o - )
↑ Klitzing, (x3x3x3x3x3x4o - )

References

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 Wiley: Kaleidoscopes: Selected Writings of H.S.M. Coxeter
  - (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)". x3o3o3o3o3x4o, x3x3o3o3o3x4o, x3o3x3o3o3x4o, x3x3x3oxo3x4o, x3o3o3x3o3x4o, x3x3o3x3o3x4o, x3o3x3x3o3x4o, x3x3x3x3o3x4o, x3o3o3o3x3x4o, x3x3o3o3x3x4o, x3o3x3o3x3x4o, x3x3x3o3x3x4o, x3o3o3x3x3x4o, x3x3o3x3x3x4o, x3o3x3x3x3x4o, x3x3x3x3x3x3o

External links

v t e Fundamental convex regular and uniform polytopes in dimensions 2–10
Family	A_n	B_n	I₂(p) / D_n	E₆ / E₇ / E₈ / F₄ / G₂	H_n
Regular polygon	Triangle	Square	p-gon	Hexagon	Pentagon
Uniform polyhedron	Tetrahedron	Octahedron • Cube	Demicube		Dodecahedron • Icosahedron
Uniform polychoron	Pentachoron	16-cell • Tesseract	Demitesseract	24-cell	120-cell • 600-cell
Uniform 5-polytope	5-simplex	5-orthoplex • 5-cube	5-demicube
Uniform 6-polytope	6-simplex	6-orthoplex • 6-cube	6-demicube	1₂₂ • 2₂₁
Uniform 7-polytope	7-simplex	7-orthoplex • 7-cube	7-demicube	1₃₂ • 2₃₁ • 3₂₁
Uniform 8-polytope	8-simplex	8-orthoplex • 8-cube	8-demicube	1₄₂ • 2₄₁ • 4₂₁
Uniform 9-polytope	9-simplex	9-orthoplex • 9-cube	9-demicube
Uniform 10-polytope	10-simplex	10-orthoplex • 10-cube	10-demicube
Uniform n-polytope	n-simplex	n-orthoplex • n-cube	n-demicube	1_k2 • 2_k1 • k₂₁	n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds

[1] Klitzing, (x3o3o3o3o3x4o - )

[2] Klitzing, (x3x3o3o3o3x4o - )

[3] Klitzing, (x3o3x3o3o3x4o - )

[4] Klitzing, (x3x3x3oxo3x4o - )

[5] Klitzing, (x3o3o3x3o3x4o - )

[6] Klitzing, (x3x3o3x3o3x4o - )

[7] Klitzing, (x3o3x3x3o3x4o - )

[8] Klitzing, (x3x3x3x3o3x4o - )

[9] Klitzing, (x3o3o3o3x3x4o - )

[10] Klitzing, (x3x3o3o3x3x4o - )

[11] Klitzing, (x3o3x3o3x3x4o - )

[12] Klitzing, (x3x3x3o3x3x4o - )

[13] Klitzing, (x3o3o3x3x3x4o - )

[14] Klitzing, (x3x3o3x3x3x4o - )

[15] Klitzing, (x3o3x3x3x3x4o - )

[16] Klitzing, (x3x3x3x3x3x4o - )

[1]

[2]

[3]

[4]

[5]

[6]

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[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

Pentellated 7-cubes

Pentellated 7-cube

Alternate names

Images

Pentitruncated 7-cube

Alternate names

Images

Penticantellated 7-cube

Alternate names

Images

Penticantitruncated 7-cube

Alternate names

Pentiruncinated 7-cube

Alternate names

Images

Pentiruncitruncated 7-cube

Alternate names

Images

Pentiruncicantellated 7-cube

Alternate names

Images

Pentiruncicantitruncated 7-cube

Alternate names

Images

Pentistericated 7-cube

Alternate names

Images

Pentisteritruncated 7-cube

Alternate names

Images

Pentistericantellated 7-cube

Alternate names

Images

Pentistericantitruncated 7-cube

Alternate names

Images

Pentisteriruncinated 7-cube

Alternate names

Images

Pentisteriruncitruncated 7-cube

Alternate names

Images

Pentisteriruncicantellated 7-cube

Alternate names

Images

Pentisteriruncicantitruncated 7-cube

Alternate names

Images

Related polytopes

Notes

References

External links

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