Stericated 7-orthoplexes
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(Redirected from Bisteritruncated 7-orthoplex)
In seven-dimensional geometry, a stericated 7-orthoplex is a convex uniform 7-polytope with 4th order truncations (sterication) of the regular 7-orthoplex. 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
Alternate names
- Small cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[1]
Images
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | File:7-cube t26.svg | File:7-cube t26 B6.svg | File:7-cube t26 B5.svg |
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | File:7-cube t26 B4.svg | File:7-cube t26 B3.svg | File:7-cube t26 B2.svg |
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | File:7-cube t26 A5.svg | File:7-cube t26 A3.svg | |
Dihedral symmetry | [6] | [4] |
Steritruncated 7-orthoplex
Alternate names
- Cellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[2]
Images
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | File:7-cube t256.svg | File:7-cube t256 B6.svg | File:7-cube t256 B5.svg |
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | File:7-cube t256 B4.svg | File:7-cube t256 B3.svg | File:7-cube t256 B2.svg |
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | File:7-cube t256 A5.svg | File:7-cube t256 A3.svg | |
Dihedral symmetry | [6] | [4] |
Bisteritruncated 7-orthoplex
Alternate names
- Bicellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[3]
Images
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | File:7-cube t145.svg | File:7-cube t145 B6.svg | File:7-cube t145 B5.svg |
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | File:7-cube t145 B4.svg | File:7-cube t145 B3.svg | File:7-cube t145 B2.svg |
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | File:7-cube t145 A5.svg | File:7-cube t145 A3.svg | |
Dihedral symmetry | [6] | [4] |
Stericantellated 7-orthoplex
Alternate names
- Cellirhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[4]
Images
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | File:7-cube t246.svg | File:7-cube t246 B6.svg | File:7-cube t246 B5.svg |
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | File:7-cube t246 B4.svg | File:7-cube t246 B3.svg | File:7-cube t246 B2.svg |
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | File:7-cube t246 A5.svg | File:7-cube t246 A3.svg | |
Dihedral symmetry | [6] | [4] |
Stericantitruncated 7-orthoplex
stericantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,4{35,4} |
Coxeter-Dynkin diagrams | File:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png File:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.png |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Celligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[5]
Images
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | File:7-cube t2456.svg | File:7-cube t2456 B6.svg | File:7-cube t2456 B5.svg |
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | File:7-cube t2456 B4.svg | File:7-cube t2456 B3.svg | File:7-cube t2456 B2.svg |
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | File:7-cube t2456 A5.svg | File:7-cube t2456 A3.svg | |
Dihedral symmetry | [6] | [4] |
Bistericantitruncated 7-orthoplex
bistericantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,3,5{35,4} |
Coxeter-Dynkin diagrams | File:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 4.pngFile:CDel node.png File:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes 11.png |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Bicelligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[6]
Images
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | File:7-cube t1345.svg | File:7-cube t1345 B6.svg | File:7-cube t1345 B5.svg |
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | File:7-cube t1345 B4.svg | File:7-cube t1345 B3.svg | File:7-cube t1345 B2.svg |
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | File:7-cube t1345 A5.svg | File:7-cube t1345 A3.svg | |
Dihedral symmetry | [6] | [4] |
Steriruncinated 7-orthoplex
Alternate names
- Celliprismated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[7]
Images
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | too complex | File:7-cube t236 B6.svg | File:7-cube t236 B5.svg |
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | File:7-cube t236 B4.svg | File:7-cube t236 B3.svg | File:7-cube t236 B2.svg |
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | File:7-cube t236 A5.svg | File:7-cube t236 A3.svg | |
Dihedral symmetry | [6] | [4] |
Steriruncitruncated 7-orthoplex
steriruncitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,3,4{35,4} |
Coxeter-Dynkin diagrams | File:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png File:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.png |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Celliprismatotruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[8]
Images
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | File:7-cube t2356.svg | File:7-cube t2356 B6.svg | File:7-cube t2356 B5.svg |
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | File:7-cube t2356 B4.svg | File:7-cube t2356 B3.svg | File:7-cube t2356 B2.svg |
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | File:7-cube t2356 A5.svg | File:7-cube t2356 A3.svg | |
Dihedral symmetry | [6] | [4] |
Steriruncicantellated 7-orthoplex
steriruncicantellated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,3,4{35,4} |
Coxeter-Dynkin diagrams | File:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png File:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.png |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Celliprismatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[9]
Images
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | File:7-cube t2346.svg | File:7-cube t2346 B6.svg | File:7-cube t2346 B5.svg |
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | File:7-cube t2346 B4.svg | File:7-cube t2346 B3.svg | File:7-cube t2346 B2.svg |
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | File:7-cube t2346 A5.svg | File:7-cube t2346 A3.svg | |
Dihedral symmetry | [6] | [4] |
Steriruncicantitruncated 7-orthoplex
steriruncicantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,4{35,4} |
Coxeter-Dynkin diagrams | File:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png File:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.png |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
- Great cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[10]
Images
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | File:7-cube t23456.svg | File:7-cube t23456 B6.svg | File:7-cube t23456 B5.svg |
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | File:7-cube t23456 B4.svg | File:7-cube t23456 B3.svg | File:7-cube t23456 B2.svg |
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | File:7-cube t23456 A5.svg | File:7-cube t23456 A3.svg | |
Dihedral symmetry | [6] | [4] |
Notes
- ↑ Klitizing, (x3o3o3o3x3o4o - )
- ↑ Klitizing, (x3x3o3o3x3o4o - )
- ↑ Klitizing, (o3x3x3o3o3x4o - )
- ↑ Klitizing, (x3o3x3o3x3o4o - )
- ↑ Klitizing, (x3x3x3o3x3o4o - )
- ↑ Klitizing, (o3x3x3x3o3x4o - )
- ↑ Klitizing, (x3o3o3x3x3o4o - )
- ↑ Klitizing, (x3x3x3o3x3o4o - )
- ↑ Klitizing, (x3o3x3x3x3o4o - )
- ↑ Klitizing, (x3x3x3x3x3o4o - )
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 [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)".