Truncated_7-simplex

Truncated 7-simplexes

Uniform 7-polytope

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

More information Orthogonal projections in A7 Coxeter plane ...

There are unique 3 degrees of truncation. Vertices of the truncation 7-simplex are located as pairs on the edge of the 7-simplex. Vertices of the bitruncated 7-simplex are located on the triangular faces of the 7-simplex. Vertices of the tritruncated 7-simplex are located inside the tetrahedral cells of the 7-simplex.

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[1] [1]
Klitizing, (x3x3o3o3o3o3o - toc)

[2] [2]
Klitizing, (o3x3x3o3o3o3o - roc)

[3] [3]
Klitizing, (o3o3x3x3o3o3o - tattoc)

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[2]

[3]

Orthogonal projections in A₇ Coxeter plane
7-simplex	Truncated 7-simplex
Bitruncated 7-simplex	Tritruncated 7-simplex

Truncated 7-simplex
Type	uniform 7-polytope
Schläfli symbol	t{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces	16
5-faces
4-faces
Cells	350
Faces	336
Edges	196
Vertices	56
Vertex figure	( )v{3,3,3,3}
Coxeter groups	A₇, [3,3,3,3,3,3]
Properties	convex, Vertex-transitive

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]

Bitruncated 7-simplex
Type	uniform 7-polytope
Schläfli symbol	2t{3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges	588
Vertices	168
Vertex figure	{ }v{3,3,3}
Coxeter groups	A₇, [3,3,3,3,3,3]
Properties	convex, Vertex-transitive

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]

Truncated_7-simplex

Truncated 7-simplexes

Truncated 7-simplex

Alternate names

Coordinates

Images

Bitruncated 7-simplex

Alternate names

Coordinates

Images

Tritruncated 7-simplex

Alternate names

Coordinates

Images

Related polytopes

See also

Notes

References

External links

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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