Stericated 7-cubes
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Orthogonal projections in B6 Coxeter plane | ||
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![]() 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Stericated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bistericated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steritruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisteritruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Stericantellated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bistericantellated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Stericantitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bistericantitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncinated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncicantellated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisteriruncitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncicantitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisteriruncicantitruncated 7-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
In seven-dimensional geometry, a stericated 7-cube is a convex uniform 7-polytope with 4th-order truncations (sterication) of the regular 7-cube.
There are 24 unique sterication for the 7-cube with permutations of truncations, cantellations, and runcinations. 10 are more simply constructed from the 7-orthoplex.
This polytope is one of 127 uniform 7-polytopes with B7 symmetry.
Stericated 7-cube
[edit]Stericated 7-cube | |
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Type | uniform 7-polytope |
Schläfli symbol | t0,4{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
[edit]- Small cellated hepteract (acronym: ) (Jonathan Bowers)[1]
Images
[edit]Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | ![]() |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | ![]() |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | ![]() |
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Dihedral symmetry | [6] | [4] |
Bistericated 7-cube
[edit]bistericated 7-cube | |
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Type | uniform 7-polytope |
Schläfli symbol | t1,5{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
[edit]- Small bicellated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)[2]
Images
[edit]Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | ![]() |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | ![]() |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | ![]() |
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Dihedral symmetry | [6] | [4] |
Steritruncated 7-cube
[edit]steritruncated 7-cube | |
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Type | uniform 7-polytope |
Schläfli symbol | t0,1,4{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
[edit]- Cellitruncated hepteract (acronym: ) (Jonathan Bowers)[3]
Images
[edit]Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | ![]() |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | ![]() |
![]() |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | ![]() |
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Dihedral symmetry | [6] | [4] |
Bisteritruncated 7-cube
[edit]bisteritruncated 7-cube | |
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Type | uniform 7-polytope |
Schläfli symbol | t1,2,5{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
[edit]- Bicellitruncated hepteract (acronym: ) (Jonathan Bowers)[4]
Images
[edit]Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | ![]() |
![]() |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | ![]() |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | ![]() |
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Dihedral symmetry | [6] | [4] |
Stericantellated 7-cube
[edit]Stericantellated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,4{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
[edit]- Cellirhombated hepteract (acronym: ) (Jonathan Bowers)[5]
Images
[edit]Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | ![]() |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | ![]() |
![]() |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | ![]() |
![]() | |
Dihedral symmetry | [6] | [4] |
Bistericantellated 7-cube
[edit]Bistericantellated 7-cube | |
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Type | uniform 7-polytope |
Schläfli symbol | t1,3,5{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
[edit]- Bicellirhombihepteract (acronym: ) (Jonathan Bowers)[6]
Images
[edit]Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | ![]() |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | ![]() |
![]() |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | ![]() |
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Dihedral symmetry | [6] | [4] |
Stericantitruncated 7-cube
[edit]stericantitruncated 7-cube | |
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Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,4{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
[edit]- Celligreatorhombated hepteract (acronym: ) (Jonathan Bowers)[7]
Images
[edit]Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | ![]() |
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Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | ![]() |
![]() |
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Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | ![]() |
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Dihedral symmetry | [6] | [4] |
Bistericantitruncated 7-cube
[edit]bistericantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,3,5{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
[edit]- Bicelligreatorhombated hepteract (acronym: ) (Jonathan Bowers)[8]
Images
[edit]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 | ![]() |
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Dihedral symmetry | [6] | [4] |
Steriruncinated 7-cube
[edit]Steriruncinated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,3,4{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
[edit]- Celliprismated hepteract (acronym: ) (Jonathan Bowers)[9]
Images
[edit]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] |
Steriruncitruncated 7-cube
[edit]steriruncitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,3,4{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
[edit]- Celliprismatotruncated hepteract (acronym: ) (Jonathan Bowers)[10]
Images
[edit]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 | ![]() |
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Dihedral symmetry | [6] | [4] |
Steriruncicantellated 7-cube
[edit]steriruncicantellated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,3,4{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
[edit]- Celliprismatorhombated hepteract (acronym: ) (Jonathan Bowers)[11]
Images
[edit]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] |
Bisteriruncitruncated 7-cube
[edit]bisteriruncitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,4,5{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
[edit]- Bicelliprismatotruncated hepteractihecatonicosoctaexon (acronym: ) (Jonathan Bowers)[12]
Images
[edit]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] |
Steriruncicantitruncated 7-cube
[edit]steriruncicantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,4{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
[edit]- Great cellated hepteract (acronym: ) (Jonathan Bowers)[13]
Images
[edit]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] |
Bisteriruncicantitruncated 7-cube
[edit]bisteriruncicantitruncated 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,3,4,5{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
[edit]- Great bicellated hepteractihecatonicosoctaexon (Acronym ) (Jonathan Bowers) [14]
Images
[edit]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
[edit]- ^ Klitizing, (x3o3o3o3x3o4o - )
- ^ Klitizing, (x3o3x3o3x3o4o - )
- ^ Klitizing, (x3x3o3o3x3o4o - )
- ^ Klitizing, (o3x3x3o3o3x4o - )
- ^ Klitizing, (x3o3x3o3x3o4o - )
- ^ Klitizing, (o3x3o3x3o3x4o - )
- ^ Klitizing, (x3x3x3o3x3o4o - )
- ^ Klitizing, (o3x3x3x3o3x4o - )
- ^ Klitizing, (x3o3o3x3x3o4o - )
- ^ Klitizing, (x3x3x3o3x3o4o - )
- ^ Klitizing, (x3o3x3x3x3o4o - )
- ^ Klitizing, (o3x3x3o3x3x4o - )
- ^ Klitizing, (x3x3x3x3x3o4o - )
- ^ Klitizing, (o3x3x3x3x3x4o - )
References
[edit]- 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 [1]
- (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, Ph.D.
- Klitzing, Richard. "7D uniform polytopes (polyexa)". x3o3o3o3x3o4o - , x3o3x3o3x3o4o - , x3x3o3o3x3o4o - , o3x3x3o3o3x4o - , x3o3x3o3x3o4o - , o3x3o3x3o3x4o - , x3x3x3o3x3o4o - , o3x3x3x3o3x4o - , x3o3o3x3x3o4o - , x3x3x3o3x3o4o - , x3o3x3x3x3o4o - , o3x3x3o3x3x4o - , x3x3x3x3x3o4o - , o3x3x3x3x3x4o -