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 |
Bisteriruncitruncated 7-orthoplex |
Steriruncicantitruncated 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
editStericated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
edit- Small cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[1]
Images
editCoxeter 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
editsteritruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
edit- Cellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[2]
Images
editCoxeter 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
editbisteritruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,5{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
edit- Bicellitruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[3]
Images
editCoxeter 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] |
Stericantellated 7-orthoplex
editStericantellated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
edit- Cellirhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[4]
Images
editCoxeter 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] |
Stericantitruncated 7-orthoplex
editstericantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
edit- Celligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[5]
Images
editCoxeter 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] |
Bistericantitruncated 7-orthoplex
editbistericantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1,2,3,5{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
edit- Bicelligreatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[6]
Images
editCoxeter 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] |
Steriruncinated 7-orthoplex
editSteriruncinated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
edit- Celliprismated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[7]
Images
editCoxeter 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] |
Steriruncitruncated 7-orthoplex
editsteriruncitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
edit- Celliprismatotruncated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[8]
Images
editCoxeter 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] |
Steriruncicantellated 7-orthoplex
editsteriruncicantellated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,2,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
edit- Celliprismatorhombated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[9]
Images
editCoxeter 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-orthoplex
editsteriruncicantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,1,2,3,4{35,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,35] |
Properties | convex |
Alternate names
edit- Great cellated hecatonicosoctaexon (acronym: ) (Jonathan Bowers)[10]
Images
editCoxeter 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] |
Notes
edit- ^ Klitizing, (x3o3o3o3x3o4o - )
- ^ Klitizing, (x3x3o3o3x3o4o - )
- ^ Klitizing, (o3x3x3o3o3x4o - )
- ^ Klitizing, (x3o3x3o3x3o4o - )
- ^ Klitizing, (x3x3x3o3x3o4o - )
- ^ Klitizing, (o3x3x3x3o3x4o - )
- ^ Klitizing, (x3o3o3x3x3o4o - )
- ^ Klitizing, (x3x3x3o3x3o4o - )
- ^ Klitizing, (x3o3x3x3x3o4o - )
- ^ Klitizing, (x3x3x3x3x3o4o - )
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)".