Stericated 7-orthoplexes

In seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-orthoplex.

More information Orthogonal projections in B6 Coxeter plane ...

Orthogonal projections in B₆ Coxeter plane
7-orthoplex	Stericated 7-orthoplex	Steritruncated 7-orthoplex
Bisteritruncated 7-orthoplex	Stericantellated 7-orthoplex	Stericantitruncated 7-orthoplex
Bistericantitruncated 7-orthoplex	Steriruncinated 7-orthoplex	Steriruncitruncated 7-orthoplex
Steriruncicantellated 7-orthoplex	Steriruncicantitruncated 7-orthoplex

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There are 24 unique sterication for the 7-orthoplex with permutations of truncations, cantellations, and runcinations. 14 are more simply constructed from the 7-cube. This polytope is one of 127 uniform 7-polytopes with B₇ symmetry.

Stericated 7-orthoplex
Type	uniform 7-polytope
Schläfli symbol	t_0,4{3⁵,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

Steritruncated 7-orthoplex
Type	uniform 7-polytope
Schläfli symbol	t_0,1,4{3⁵,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

Bisteritruncated 7-orthoplex
Type	uniform 7-polytope
Schläfli symbol	t_1,2,5{3⁵,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups	B₇, [4,3⁵]
Properties	convex

Stericated 7-orthoplexes

Stericated 7-orthoplex

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Steritruncated 7-orthoplex

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Images

Bisteritruncated 7-orthoplex

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Images

Stericantellated 7-orthoplex

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Images

Stericantitruncated 7-orthoplex

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Images

Bistericantitruncated 7-orthoplex

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Images

Steriruncinated 7-orthoplex

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Images

Steriruncitruncated 7-orthoplex

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Images

Steriruncicantellated 7-orthoplex

Alternate names

Images

Steriruncicantitruncated 7-orthoplex

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Images

Notes

References

External links

Related Articles

Coxeter plane	B₇ / A₆	B₆ / D₇	B₅ / D₆ / A₄
Graph	too complex
Dihedral symmetry	[14]	[12]	[10]
Coxeter plane	B₄ / D₅	B₃ / D₄ / A₂	B₂ / D₃
Graph
Dihedral symmetry	[8]	[6]	[4]
Coxeter plane	A₅	A₃
Graph
Dihedral symmetry	[6]	[4]

v t e Fundamental convex regular and uniform polytopes in dimensions 2–10
Family	$A n$	$B n$	$I 2 (p)$ / $D n$	$E 6$ / $E 7$ / $E 8$ / $F 4$ / $G 2$	$H n$
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 • Polytope operations