6-cube
   
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Stericated 6-cube
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Steritruncated 6-cube
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Stericantellated 6-cube
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Stericantitruncated 6-cube
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Steriruncinated 6-cube
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Steriruncitruncated 6-cube
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Steriruncicantellated 6-cube
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Steriruncicantitruncated 6-cube
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| 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.
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 [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. "6D uniform polytopes (polypeta)". https://bendwavy.org/klitzing/dimensions/polypeta.htm.
External links
 | Original source: https://en.wikipedia.org/wiki/Stericated 6-cubes. Read more |
