Pentistericated_7-orthoplex

Pentellated 7-orthoplexes

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

More information Orthogonal projections in B6 Coxeter plane ...

There are 32 unique pentellations of the 7-orthoplex with permutations of truncations, cantellations, runcinations, and sterications. 16 are more simply constructed relative to the 7-cube.

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

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This article uses material from the Wikipedia article Pentistericated_7-orthoplex, and is written by contributors. Text is available under a CC BY-SA 4.0 International License; additional terms may apply. Images, videos and audio are available under their respective licenses.

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Orthogonal projections in B₆ Coxeter plane
7-orthoplex	Pentellated 7-orthoplex	Pentitruncated 7-orthoplex	Penticantellated 7-orthoplex
Penticantitruncated 7-orthoplex	Pentiruncinated 7-orthoplex	Pentiruncitruncated 7-orthoplex	Pentiruncicantellated 7-orthoplex
Pentiruncicantitruncated 7-orthoplex	Pentistericated 7-orthoplex	Pentisteritruncated 7-orthoplex	Pentistericantellated 7-orthoplex
Pentistericantitruncated 7-orthoplex	Pentisteriruncinated 7-orthoplex	Pentisteriruncitruncated 7-orthoplex	Pentisteriruncicantellated 7-orthoplex
Pentisteriruncicantitruncated 7-orthoplex

Pentellated 7-orthoplex
Type	uniform 7-polytope
Schläfli symbol	t_0,5{3⁵,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges	20160
Vertices	2688
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

pentitruncated 7-orthoplex
Type	uniform 7-polytope
Schläfli symbol	t_0,1,5{3⁵,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges	87360
Vertices	13440
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	too complex
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

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

Pentistericated_7-orthoplex

Pentellated 7-orthoplex

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Pentitruncated 7-orthoplex

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Penticantellated 7-orthoplex

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Penticantitruncated 7-orthoplex

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Pentiruncinated 7-orthoplex

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Pentiruncitruncated 7-orthoplex

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Pentiruncicantellated 7-orthoplex

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Pentiruncicantitruncated 7-orthoplex

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