Bicantellated_6-cube

Cantellated 6-cubes

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In six-dimensional geometry, a cantellated 6-cube is a convex uniform 6-polytope, being a cantellation of the regular 6-cube.

More information Orthogonal projections in B6 Coxeter plane ...

There are 8 cantellations for the 6-cube, including truncations. Half of them are more easily constructed from the dual 5-orthoplex.

Cantellated 6-cube

Cantellated 6-cube
Type	uniform 6-polytope
Schläfli symbol	rr{4,3,3,3,3} or $r\left\{{\begin{array}{l}3,3,3,3\\4\end{array}}\right\}$
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges	4800
Vertices	960
Vertex figure
Coxeter groups	B₆, [3,3,3,3,4]
Properties	convex

Bicantellated 6-cube

Cantellated 6-cube
Type	uniform 6-polytope
Schläfli symbol	2rr{4,3,3,3,3} or $r\left\{{\begin{array}{l}3,3,3\\3,4\end{array}}\right\}$
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₆, [3,3,3,3,4]
Properties	convex

Cantitruncated 6-cube

Cantellated 6-cube
Type	uniform 6-polytope
Schläfli symbol	tr{4,3,3,3,3} or $t\left\{{\begin{array}{l}3,3,3,3\\4\end{array}}\right\}$
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₆, [3,3,3,3,4]
Properties	convex

Bicantitruncated 6-cube

Cantellated 6-cube
Type	uniform 6-polytope
Schläfli symbol	2tr{4,3,3,3,3} or $t\left\{{\begin{array}{l}3,3,3\\3,4\end{array}}\right\}$
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₆, [3,3,3,3,4]
Properties	convex

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This article uses material from the Wikipedia article Bicantellated_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, (o3o3o3x3o4x - srox)

[2] [2]
Klitzing, (o3o3x3o3x4o - saborx)

[3] [3]
Klitzing, (o3o3o3x3x4x - grox)

[4] [4]
Klitzing, (o3o3x3x3x4o - gaborx)

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[2]

[3]

[4]

Orthogonal projections in B₆ Coxeter plane
6-cube		Cantellated 6-cube		Bicantellated 6-cube
6-orthoplex		Cantellated 6-orthoplex		Bicantellated 6-orthoplex
Cantitruncated 6-cube	Bicantitruncated 6-cube		Bicantitruncated 6-orthoplex		Cantitruncated 6-orthoplex

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]

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]

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]


Truncated cuboctahedron	Cantitruncated tesseract	Cantitruncated 5-cube	Cantitruncated 6-cube	Cantitruncated 7-cube	Cantitruncated 8-cube

Bicantellated_6-cube

Cantellated 6-cubes

Cantellated 6-cube

Alternate names

Images

Bicantellated 6-cube

Alternate names

Images

Cantitruncated 6-cube

Alternate names

Images

Bicantitruncated 6-cube

Alternate names

Images

Related polytopes

Notes

References

External links

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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