Runcinated 6-orthoplexes
In six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex.
6-cube |
Runcinated 6-cube |
Biruncinated 6-cube |
Runcinated 6-orthoplex |
6-orthoplex |
Runcitruncated 6-cube |
Biruncitruncated 6-cube |
Runcicantellated 6-orthoplex |
Runcicantellated 6-cube |
Biruncitruncated 6-orthoplex |
Runcitruncated 6-orthoplex |
Runcicantitruncated 6-cube |
Biruncicantitruncated 6-cube |
Runcicantitruncated 6-orthoplex | |
Orthogonal projections in BC6 Coxeter plane |
---|
There are 12 unique runcinations of the 6-orthoplex with permutations of truncations, and cantellations. Half are expressed relative to the dual 6-cube.
Runcinated 6-orthoplex
Alternate names
- Small prismatohexacontatetrapeton (spog) (Jonathan Bowers)[1]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Runcicantellated 6-orthoplex
Alternate names
- Prismatorhombated hexacontatetrapeton (prog) (Jonathan Bowers)[2]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Runcitruncated 6-orthoplex
Alternate names
- Prismatotruncated hexacontatetrapeton (potag) (Jonathan Bowers)[3]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Biruncicantellated 6-cube
Alternate names
- Great biprismated hexeractihexacontatetrapeton (gobpoxog) (Jonathan Bowers)[4]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Related polytopes
These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.
Notes
- Klitzing, (x3o3o3x3o4o - spog)
- Klitzing, (x3o3x3x3o4o - prog)
- Klitzing, (x3x3o3x3o4o - potag)
- Klitzing, (o3x3x3x3x4o - gobpoxog)
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, Ph.D.
- Klitzing, Richard. "6D uniform polytopes (polypeta)". x3o3o3x3o4o - spog, x3o3x3x3o4o - prog, x3x3o3x3o4o - potag, o3x3x3x3x4o - gobpoxog
External links
- Weisstein, Eric W. "Hypercube". MathWorld.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary
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