Stericated 6-cubes
6-cube
|
Stericated 6-cube
|
Steritruncated 6-cube
|
Stericantellated 6-cube
|
Stericantitruncated 6-cube
|
Steriruncinated 6-cube
|
Steriruncitruncated 6-cube
|
Steriruncicantellated 6-cube
|
Steriruncicantitruncated 6-cube
|
Orthogonal projections in B6 Coxeter plane |
In six-dimensional geometry, a stericated 6-cube is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-cube.
There are 8 unique sterications for the 6-cube with permutations of truncations, cantellations, and runcinations.
Stericated 6-cube
Alternate names
- Small cellated hexeract (Acronym: scox) (Jonathan Bowers)[1]
Images
Steritruncated 6-cube
Steritruncated 6-cube |
Type | uniform 6-polytope |
Schläfli symbol | t0,1,4{4,3,3,3,3} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 19200 |
Vertices | 3840 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)[2]
Images
Stericantellated 6-cube
Alternate names
- Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)[3]
Images
Stericantitruncated 6-cube
stericantitruncated 6-cube |
Type | uniform 6-polytope |
Schläfli symbol | t0,1,2,4{4,3,3,3,3} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 46080 |
Vertices | 11520 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)[4]
Images
Steriruncinated 6-cube
steriruncinated 6-cube |
Type | uniform 6-polytope |
Schläfli symbol | t0,3,4{4,3,3,3,3} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 15360 |
Vertices | 3840 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)[5]
Images
Steriruncitruncated 6-cube
Alternate names
- Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)[6]
Images
Steriruncicantellated 6-cube
steriruncicantellated 6-cube |
Type | uniform 6-polytope |
Schläfli symbol | t0,2,3,4{4,3,3,3,3} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 40320 |
Vertices | 11520 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)[7]
Images
Steriruncicantitruncated 6-cube
Alternate names
- Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)[8]
Images
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.
B6 polytopes |
β6 |
t1β6 |
t2β6 |
t2γ6 |
t1γ6 |
γ6 |
t0,1β6 |
t0,2β6 |
t1,2β6 |
t0,3β6 |
t1,3β6 |
t2,3γ6 |
t0,4β6 |
t1,4γ6 |
t1,3γ6 |
t1,2γ6 |
t0,5γ6 |
t0,4γ6 |
t0,3γ6 |
t0,2γ6 |
t0,1γ6 |
t0,1,2β6 |
t0,1,3β6 |
t0,2,3β6 |
t1,2,3β6 |
t0,1,4β6 |
t0,2,4β6 |
t1,2,4β6 |
t0,3,4β6 |
t1,2,4γ6 |
t1,2,3γ6 |
t0,1,5β6 |
t0,2,5β6 |
t0,3,4γ6 |
t0,2,5γ6 |
t0,2,4γ6 |
t0,2,3γ6 |
t0,1,5γ6 |
t0,1,4γ6 |
t0,1,3γ6 |
t0,1,2γ6 |
t0,1,2,3β6 |
t0,1,2,4β6 |
t0,1,3,4β6 |
t0,2,3,4β6 |
t1,2,3,4γ6 |
t0,1,2,5β6 |
t0,1,3,5β6 |
t0,2,3,5γ6 |
t0,2,3,4γ6 |
t0,1,4,5γ6 |
t0,1,3,5γ6 |
t0,1,3,4γ6 |
t0,1,2,5γ6 |
t0,1,2,4γ6 |
t0,1,2,3γ6 |
t0,1,2,3,4β6 |
t0,1,2,3,5β6 |
t0,1,2,4,5β6 |
t0,1,2,4,5γ6 |
t0,1,2,3,5γ6 |
t0,1,2,3,4γ6 |
t0,1,2,3,4,5γ6 |
Notes
- ↑ Klitzing, (x4o3o3o3x3o - scox)
- ↑ Klitzing, (x4x3o3o3x3o - catax)
- ↑ Klitzing, (x4o3x3o3x3o - crax)
- ↑ Klitzing, (x4x3x3o3x3o - cagorx)
- ↑ Klitzing, (x4o3o3x3x3o - copox))
- ↑ Klitzing, (x4x3o3x3x3o - captix)
- ↑ Klitzing, (x4o3x3x3x3o - coprix)
- ↑ Klitzing, (x4x3x3x3x3o - gocax)
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)".
External links