Pentellated_6-cube

Pentellated 6-cubes

Add article description

In six-dimensional geometry, a pentellated 6-cube is a convex uniform 6-polytope with 5th order truncations of the regular 6-cube.

More information Orthogonal projections in B6 Coxeter plane ...

There are unique 16 degrees of pentellations of the 6-cube with permutations of truncations, cantellations, runcinations, and sterications. The simple pentellated 6-cube is also called an expanded 6-cube, constructed by an expansion operation applied to the regular 6-cube. The highest form, the pentisteriruncicantitruncated 6-cube, is called an omnitruncated 6-cube with all of the nodes ringed. Six of them are better constructed from the 6-orthoplex given at pentellated 6-orthoplex.

Share this article:

This article uses material from the Wikipedia article Pentellated_6-cube, 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.

[1] [1]
Klitzing, (x4o3o3o3o3x - stoxog)

[2] [2]
Klitzing, (x4x3o3o3o3x - tacog)

[3] [3]
Klitzing, (x4o3x3o3o3x - topag)

[4] [4]
Klitzing, (x4x3x3o3o3x - togrix)

[5] [5]
Klitzing, (x4x3o3x3o3x - tocrag)

[6] [6]
Klitzing, (x4o3x3x3o3x - tiprixog)

[7] [7]
Klitzing, (x4x3x3o3x3x - tagpox)

[8] [8]
Klitzing, (x4x3o3o3x3x - tactaxog)

[9] [9]
Klitzing, (x4x3x3o3x3x - tocagrax)

[10] [10]
Klitzing, (x4x3x3x3x3x - gotaxog)

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

Orthogonal projections in B₆ Coxeter plane
6-cube	6-orthoplex	Pentellated 6-cube
Pentitruncated 6-cube	Penticantellated 6-cube	Penticantitruncated 6-cube
Pentiruncitruncated 6-cube	Pentiruncicantellated 6-cube	Pentiruncicantitruncated 6-cube
Pentisteritruncated 6-cube	Pentistericantitruncated 6-cube	Omnitruncated 6-cube

Pentellated 6-cube
Type	Uniform 6-polytope
Schläfli symbol	t_0,5{4,3,3,3,3}
Coxeter-Dynkin diagram
5-faces
4-faces
Cells
Faces
Edges	1920
Vertices	384
Vertex figure	5-cell antiprism
Coxeter group	B₆, [4,3,3,3,3]
Properties	convex

Coxeter plane	B₆	B₅	B₄
Graph
Dihedral symmetry	[12]	[10]	[8]
Coxeter plane	B₃	B₂
Graph
Dihedral symmetry	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

Pentitruncated 6-cube
Type	uniform 6-polytope
Schläfli symbol	t_0,1,5{4,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges	8640
Vertices	1920
Vertex figure
Coxeter groups	B₆, [4,3,3,3,3]
Properties	convex

Coxeter plane	B₆	B₅	B₄
Graph
Dihedral symmetry	[12]	[10]	[8]
Coxeter plane	B₃	B₂
Graph
Dihedral symmetry	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

Pentellated_6-cube

Pentellated 6-cubes

Pentellated 6-cube

Alternate names

Images

Pentitruncated 6-cube

Alternate names

Images

Penticantellated 6-cube

Alternate names

Images

Penticantitruncated 6-cube

Alternate names

Images

Pentiruncitruncated 6-cube

Alternate names

Images

Pentiruncicantellated 6-cube

Alternate names

Images

Pentiruncicantitruncated 6-cube

Alternate names

Images

Pentisteritruncated 6-cube

Alternate names

Images

Pentistericantitruncated 6-cube

Alternate names

Images

Omnitruncated 6-cube

Alternate names

Images

Full snub 6-cube

Related polytopes

Notes

References

External links

Share this article:

B6 polytopes
β₆	t₁β₆	t₂β₆	t₂γ₆	t₁γ₆	γ₆	t_0,1β₆	t_0,2β₆
t_1,2β₆	t_0,3β₆	t_1,3β₆	t_2,3γ₆	t_0,4β₆	t_1,4γ₆	t_1,3γ₆	t_1,2γ₆
t_0,5γ₆	t_0,4γ₆	t_0,3γ₆	t_0,2γ₆	t_0,1γ₆	t_0,1,2β₆	t_0,1,3β₆	t_0,2,3β₆
t_1,2,3β₆	t_0,1,4β₆	t_0,2,4β₆	t_1,2,4β₆	t_0,3,4β₆	t_1,2,4γ₆	t_1,2,3γ₆	t_0,1,5β₆
t_0,2,5β₆	t_0,3,4γ₆	t_0,2,5γ₆	t_0,2,4γ₆	t_0,2,3γ₆	t_0,1,5γ₆	t_0,1,4γ₆	t_0,1,3γ₆
t_0,1,2γ₆	t_0,1,2,3β₆	t_0,1,2,4β₆	t_0,1,3,4β₆	t_0,2,3,4β₆	t_1,2,3,4γ₆	t_0,1,2,5β₆	t_0,1,3,5β₆
t_0,2,3,5γ₆	t_0,2,3,4γ₆	t_0,1,4,5γ₆	t_0,1,3,5γ₆	t_0,1,3,4γ₆	t_0,1,2,5γ₆	t_0,1,2,4γ₆	t_0,1,2,3γ₆
t_0,1,2,3,4β₆	t_0,1,2,3,5β₆	t_0,1,2,4,5β₆	t_0,1,2,4,5γ₆	t_0,1,2,3,5γ₆	t_0,1,2,3,4γ₆	t_0,1,2,3,4,5γ₆

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