Hexicated 7-cubes
Orthogonal projections in B4 Coxeter plane | |||
---|---|---|---|
7-cube |
Hexicated 7-cube |
Hexitruncated 7-cube |
Hexicantellated 7-cube |
Hexiruncinated 7-cube |
Hexicantitruncated 7-cube |
Hexiruncitruncated 7-cube |
Hexiruncicantellated 7-cube |
Hexisteritruncated 7-cube |
Hexistericantellated 7-cube |
Hexipentitruncated 7-cube |
Hexiruncicantitruncated 7-cube |
Hexistericantitruncated 7-cube |
Hexisteriruncitruncated 7-cube |
Hexisteriruncicantellated 7-cube |
Hexipenticantitruncated 7-cube |
Hexipentiruncitruncated 7-cube |
Hexisteriruncicantitruncated 7-cube |
Hexipentiruncicantitruncated 7-cube |
Hexipentistericantitruncated 7-cube |
Hexipentisteriruncicantitruncated 7-cube (Omnitruncated 7-cube) |
In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-cube.
There are 32 hexications for the 7-cube, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations. 20 are represented here, while 12 are more easily constructed from the 7-orthoplex.
The simple hexicated 7-cube is also called an expanded 7-cube, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 7-cube. The highest form, the hexipentisteriruncicantitruncated 7-cube is more simply called a omnitruncated 7-cube with all of the nodes ringed.
These polytope are among a family of 127 uniform 7-polytopes with B7 symmetry.
Hexicated 7-cube
Hexicated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
In seven-dimensional geometry, a hexicated 7-cube is a convex uniform 7-polytope, a hexication (6th order truncation) of the regular 7-cube, or alternately can be seen as an expansion operation.
Alternate names
- Small petated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexitruncated 7-cube
hexitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Petitruncated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexicantellated 7-cube
Hexicantellated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Petirhombated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexiruncinated 7-cube
Hexiruncinated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,3,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Petiprismated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexicantitruncated 7-cube
Hexicantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Petigreatorhombated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexiruncitruncated 7-cube
Hexiruncitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,3,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Petiprismatotruncated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexiruncicantellated 7-cube
Hexiruncicantellated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,3,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
In seven-dimensional geometry, a hexiruncicantellated 7-cube is a uniform 7-polytope.
Alternate names
- Petiprismatorhombated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexisteritruncated 7-cube
hexisteritruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,4,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Peticellitruncated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexistericantellated 7-cube
hexistericantellated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,4,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Peticellirhombihepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexipentitruncated 7-cube
Hexipentitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,5,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Petiteritruncated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexiruncicantitruncated 7-cube
Hexiruncicantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Petigreatoprismated hepteract (acronym: ) (Jonathan Bowers)
Images
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 | too complex | too complex | |
Dihedral symmetry | [6] | [4] |
Hexistericantitruncated 7-cube
Hexistericantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,4,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Peticelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexisteriruncitruncated 7-cube
Hexisteriruncitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,3,4,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Peticelliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexisteriruncicantellated 7-cube
Hexisteriruncitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,3,4,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Peticelliprismatorhombihepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexipenticantitruncated 7-cube
hexipenticantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,5,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Petiterigreatorhombated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexipentiruncitruncated 7-cube
Hexisteriruncicantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,4,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Great petacellated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexisteriruncicantitruncated 7-cube
Hexisteriruncicantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,4,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Great petacellated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexipentiruncicantitruncated 7-cube
Hexipentiruncicantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,5,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Petiterigreatoprismated hepteract (acronym: ) (Jonathan Bowers)
Images
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] |
Hexipentistericantitruncated 7-cube
Hexipentistericantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,4,5,6{4,35} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Petitericelligreatorhombihepteract (acronym: putcagroh) (Jonathan Bowers)
Images
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] |
Omnitruncated 7-cube
Omnitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,4,5,6{36} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
The omnitruncated 7-cube is the largest uniform 7-polytope in the B7 symmetry of the regular 7-cube. It can also be called the hexipentisteriruncicantitruncated 7-cube which is the long name for the omnitruncation for 7 dimensions, with all reflective mirrors active.
Alternate names
- Great petated hepteract (Acronym: ) (Jonathan Bowers)
Images
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] |
Notes
References
- H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
- Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6
- (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
- (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, PhD (1966)
- Klitzing, Richard. "7D uniform polytopes (polyexa)". x3o3o3o3o3o4x - , x3x3o3o3o3o3x- , x3o3o3x3o3o4x - , x3x3x3o3o3o4x - , x3x3o3x3o3o4x - , x3o3x3x3o3o4x - , x3o3x3o3o3x4x - , x3o3x3o3x3o4x - , x3x3o3o3o3x4x - , x3x3x3x3o3o4x - , x3x3x3o3x3o4x - , x3x3o3x3x3o4x - , x3o3x3x3x3o4x - , x3x3x3oxo3x4x - , x3x3x3x3x3o4x - , x3x3x3o3x3x4x - , x3x3o3x3x3x4x - , x3x3x3x3x3x4x -
External links
- Olshevsky, George. "Cross polytope". Glossary for Hyperspace. Archived from the original on 4 February 2007.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary
Fundamental convex regular and uniform polytopes in dimensions 2–10 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Family | An | Bn | I2(p) / Dn | E6 / E7 / E8 / E9 / E10 / F4 / G2 | Hn | |||||||
Regular polygon | Triangle | Square | p-gon | Hexagon | Pentagon | |||||||
Uniform polyhedron | Tetrahedron | Octahedron • Cube | Demicube | Dodecahedron • Icosahedron | ||||||||
Uniform 4-polytope | 5-cell | 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 | 1k2 • 2k1 • k21 | n-pentagonal polytope | |||||||
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds |