Hexiruncicantellated_7-simplex

Hexicated 7-simplexes

Type of 7-polytope

In seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-simplex.

More information Orthogonal projections in A7 Coxeter plane ...

There are 20 unique hexications for the 7-simplex, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations.

The simple hexicated 7-simplex is also called an expanded 7-simplex, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 7-simplex. The highest form, the hexipentisteriruncicantitruncated 7-simplex is more simply called a omnitruncated 7-simplex with all of the nodes ringed.

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Klitzing, (x3o3o3o3o3o3x - suph)

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Klitzing, (x3x3o3o3o3o3x- puto)

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Klitzing, (x3o3x3o3o3o3x - puro)

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Klitzing, (x3o3o3x3o3o3x - puph)

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Klitzing, (x3o3o3o3x3o3x - pugro)

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Klitzing, (x3x3x3o3o3o3x - pupato)

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Klitzing, (x3o3x3x3o3o3x - pupro)

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Klitzing, (x3x3o3o3x3o3x - pucto)

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Klitzing, (x3o3x3o3x3o3x - pucroh)

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Klitzing, (x3x3o3o3o3x3x - putath)

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Klitzing, (x3x3x3x3o3o3x - pugopo)

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Klitzing, (x3x3x3o3x3o3x - pucagro)

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Klitzing, (x3x3o3x3x3o3x - pucpato)

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Klitzing, (x3o3x3x3x3o3x - pucproh)

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Klitzing, (x3x3x3o3o3x3x - putagro)

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Klitzing, (x3x3o3x3o3x3x - putpath)

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Klitzing, (x3x3x3x3x3o3x - pugaco)

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Klitzing, (x3x3x3x3o3x3x - putgapo)

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Klitzing, (x3x3x3o3x3x3x - putcagroh)

[20] [20]
Klitzing, (x3x3x3x3x3x3x - guph)

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Orthogonal projections in A₇ Coxeter plane
7-simplex	Hexicated 7-simplex	Hexitruncated 7-simplex	Hexicantellated 7-simplex
Hexiruncinated 7-simplex	Hexicantitruncated 7-simplex	Hexiruncitruncated 7-simplex	Hexiruncicantellated 7-simplex
Hexisteritruncated 7-simplex	Hexistericantellated 7-simplex	Hexipentitruncated 7-simplex	Hexiruncicantitruncated 7-simplex
Hexistericantitruncated 7-simplex	Hexisteriruncitruncated 7-simplex	Hexisteriruncicantellated 7-simplex	Hexipenticantitruncated 7-simplex
Hexipentiruncitruncated 7-simplex	Hexisteriruncicantitruncated 7-simplex	Hexipentiruncicantitruncated 7-simplex	Hexipentistericantitruncated 7-simplex
Hexipentisteriruncicantitruncated 7-simplex (Omnitruncated 7-simplex)

Hexicated 7-simplex
Type	uniform 7-polytope
Schläfli symbol	t_0,6{3⁶}
Coxeter-Dynkin diagrams
6-faces	254: 8+8 {3⁵} 28+28 {}x{3⁴} 56+56 {3}x{3,3,3} 70 {3,3}x{3,3}
5-faces
4-faces
Cells
Faces
Edges	336
Vertices	56
Vertex figure	5-simplex antiprism
Coxeter group	A₇×2, [[3⁶]], order 80640
Properties	convex

A_k Coxeter plane	A₇	A₆	A₅
Graph
Dihedral symmetry	[8]	[[7]]	[6]
A_k Coxeter plane	A₄	A₃	A₂
Graph
Dihedral symmetry	[[5]]	[4]	[[3]]

hexitruncated 7-simplex
Type	uniform 7-polytope
Schläfli symbol	t_0,1,6{3⁶}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges	1848
Vertices	336
Vertex figure
Coxeter group	A₇, [3⁶], order 40320
Properties	convex

A_k Coxeter plane	A₇	A₆	A₅
Graph
Dihedral symmetry	[8]	[7]	[6]
A_k Coxeter plane	A₄	A₃	A₂
Graph
Dihedral symmetry	[5]	[4]	[3]

A7 polytopes
t₀	t₁	t₂	t₃	t_0,1	t_0,2	t_1,2	t_0,3
t_1,3	t_2,3	t_0,4	t_1,4	t_2,4	t_0,5	t_1,5	t_0,6
t_0,1,2	t_0,1,3	t_0,2,3	t_1,2,3	t_0,1,4	t_0,2,4	t_1,2,4	t_0,3,4
t_1,3,4	t_2,3,4	t_0,1,5	t_0,2,5	t_1,2,5	t_0,3,5	t_1,3,5	t_0,4,5
t_0,1,6	t_0,2,6	t_0,3,6	t_0,1,2,3	t_0,1,2,4	t_0,1,3,4	t_0,2,3,4	t_1,2,3,4
t_0,1,2,5	t_0,1,3,5	t_0,2,3,5	t_1,2,3,5	t_0,1,4,5	t_0,2,4,5	t_1,2,4,5	t_0,3,4,5
t_0,1,2,6	t_0,1,3,6	t_0,2,3,6	t_0,1,4,6	t_0,2,4,6	t_0,1,5,6	t_0,1,2,3,4	t_0,1,2,3,5
t_0,1,2,4,5	t_0,1,3,4,5	t_0,2,3,4,5	t_1,2,3,4,5	t_0,1,2,3,6	t_0,1,2,4,6	t_0,1,3,4,6	t_0,2,3,4,6
t_0,1,2,5,6	t_0,1,3,5,6	t_0,1,2,3,4,5	t_0,1,2,3,4,6	t_0,1,2,3,5,6	t_0,1,2,4,5,6	t_{0,1,2,3,4,5,6}

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

Hexiruncicantellated_7-simplex

Hexicated 7-simplex

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Hexitruncated 7-simplex

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Hexicantellated 7-simplex

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Hexiruncinated 7-simplex

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Hexicantitruncated 7-simplex

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Hexiruncitruncated 7-simplex

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