Runcinated 6-orthoplexes
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| 120px 6-cube    
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120px Runcinated 6-cube
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120px Biruncinated 6-cube
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120px Runcinated 6-orthoplex
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120px 6-orthoplex
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| 120px Runcitruncated 6-cube
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120px Biruncitruncated 6-cube
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120px Runcicantellated 6-orthoplex
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120px Runcicantellated 6-cube
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120px Biruncitruncated 6-orthoplex
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| 120px Runcitruncated 6-orthoplex
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120px Runcicantitruncated 6-cube
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120px Biruncicantitruncated 6-cube
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120px Runcicantitruncated 6-orthoplex
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| Orthogonal projections in BC6 Coxeter plane | ||||
|---|---|---|---|---|
In six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex.
There are 12 unique runcinations of the 6-orthoplex with permutations of truncations, and cantellations. 7 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] |
Biruncitruncated 6-orthoplex
Alternate names
- Biprismatotruncated hexacontatetrapeton (boprax) (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] |
Runcitruncated 6-orthoplex
Alternate names
- Prismatotruncated hexacontatetrapeton (potag) (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] |
Runcicantitruncated 6-orthoplex
Alternate names
- Great prismated hexacontatetrapeton (gopog) (Jonathan Bowers)[5]
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
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, wiley.com, 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) with acronyms". https://bendwavy.org/klitzing/dimensions/polypeta.htm. x3o3o3x3o4o - spog, x3o3x3x3o4o - prog, x3x3o3x3o4o - potag, o3x3x3o3x4o - boprax, x3x3x3x3o4o - gopog
External links
- Weisstein, Eric W.. "Hypercube". http://mathworld.wolfram.com/Hypercube.html.
- 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 / 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 | ||||||||||||
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