Bicantellated_7-simplex

Cantellated 7-simplexes

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In seven-dimensional geometry, a cantellated 7-simplex is a convex uniform 7-polytope, being a cantellation of the regular 7-simplex.

More information Orthogonal projections in A7 Coxeter plane ...

There are unique 6 degrees of cantellation for the 7-simplex, including truncations.

Cantellated 7-simplex

Cantellated 7-simplex
Type	uniform 7-polytope
Schläfli symbol	rr{3,3,3,3,3,3} or $r\left\{{\begin{array}{l}3,3,3,3,3\\3\end{array}}\right\}$
Coxeter-Dynkin diagram	or
6-faces
5-faces
4-faces
Cells
Faces
Edges	1008
Vertices	168
Vertex figure	5-simplex prism
Coxeter groups	A₇, [3,3,3,3,3,3]
Properties	convex

Bicantellated 7-simplex

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Bicantellated 7-simplex
Type	uniform 7-polytope
Schläfli symbol	r2r{3,3,3,3,3,3} or $r\left\{{\begin{array}{l}3,3,3,3\\3,3\end{array}}\right\}$
Coxeter-Dynkin diagrams	or
6-faces
5-faces
4-faces
Cells
Faces
Edges	2520
Vertices	420
Vertex figure
Coxeter groups	A₇, [3,3,3,3,3,3]
Properties	convex

Tricantellated 7-simplex

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Tricantellated 7-simplex
Type	uniform 7-polytope
Schläfli symbol	r3r{3,3,3,3,3,3} or $r\left\{{\begin{array}{l}3,3,3\\3,3,3\end{array}}\right\}$
Coxeter-Dynkin diagrams	or
6-faces
5-faces
4-faces
Cells
Faces
Edges	3360
Vertices	560
Vertex figure
Coxeter groups	A₇, [3,3,3,3,3,3]
Properties	convex

Cantitruncated 7-simplex

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Cantitruncated 7-simplex
Type	uniform 7-polytope
Schläfli symbol	tr{3,3,3,3,3,3} or $t\left\{{\begin{array}{l}3,3,3,3,3\\3\end{array}}\right\}$
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges	1176
Vertices	336
Vertex figure
Coxeter groups	A₇, [3,3,3,3,3,3]
Properties	convex

Bicantitruncated 7-simplex

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Bicantitruncated 7-simplex
Type	uniform 7-polytope
Schläfli symbol	t2r{3,3,3,3,3,3} or $t\left\{{\begin{array}{l}3,3,3,3\\3,3\end{array}}\right\}$
Coxeter-Dynkin diagrams	or
6-faces
5-faces
4-faces
Cells
Faces
Edges	2940
Vertices	840
Vertex figure
Coxeter groups	A₇, [3,3,3,3,3,3]
Properties	convex

Tricantitruncated 7-simplex

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Tricantitruncated 7-simplex
Type	uniform 7-polytope
Schläfli symbol	t3r{3,3,3,3,3,3} or $t\left\{{\begin{array}{l}3,3,3\\3,3,3\end{array}}\right\}$
Coxeter-Dynkin diagrams	or
6-faces
5-faces
4-faces
Cells
Faces
Edges	3920
Vertices	1120
Vertex figure
Coxeter groups	A₇, [3,3,3,3,3,3]
Properties	convex

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This article uses material from the Wikipedia article Bicantellated_7-simplex, 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]
Klitizing, (x3o3x3o3o3o3o - saro)

[2] [2]
Klitizing, (o3x3o3x3o3o3o - sabro)

[3] [3]
Klitizing, (o3o3x3o3x3o3o - stiroh)

[4] [4]
Klitizing, (x3x3x3o3o3o3o - garo)

[5] [5]
Klitizing, (o3x3x3x3o3o3o - gabro)

[6] [6]
Klitizing, (o3o3x3x3x3o3o - gatroh)

[1]

[2]

[3]

[4]

[5]

[6]

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]

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]

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]

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]

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]

Bicantellated_7-simplex

Cantellated 7-simplexes

Cantellated 7-simplex

Alternate names

Coordinates

Images

Bicantellated 7-simplex

Alternate names

Coordinates

Images

Tricantellated 7-simplex

Alternate names

Coordinates

Images

Cantitruncated 7-simplex

Alternate names

Coordinates

Images

Bicantitruncated 7-simplex

Alternate names

Coordinates

Images

Tricantitruncated 7-simplex

Alternate names

Coordinates

Images

Related polytopes

See also

Notes

References

External links

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Orthogonal projections in A₇ Coxeter plane
7-simplex	Cantellated 7-simplex	Bicantellated 7-simplex	Tricantellated 7-simplex
Birectified 7-simplex	Cantitruncated 7-simplex	Bicantitruncated 7-simplex	Tricantitruncated 7-simplex

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