Stericated 6-cubes
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Orthogonal projections in B6 Coxeter plane |
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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
Stericated 6-cube |
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Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Small cellated hexeract (Acronym: scox) (Jonathan Bowers)
Steritruncated 6-cube
Steritruncated 6-cube |
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Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Cellirhombated hexeract (Acronym: catax) (Jonathan Bowers)
Stericantellated 6-cube
Stericantellated 6-cube |
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Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Cellirhombated hexeract (Acronym: crax) (Jonathan Bowers)
Stericantitruncated 6-cube
Stericantitruncated 6-cube |
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Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Celligreatorhombated hexeract (Acronym: cagorx) (Jonathan Bowers)
Steriruncinated 6-cube
Steriruncinated 6-cube |
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Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Celliprismated hexeract (Acronym: copox) (Jonathan Bowers)
Steriruncitruncated 6-cube
Steriruncitruncated 6-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Celliprismatotruncated hexeract (Acronym: captix) (Jonathan Bowers)
Steriruncicantellated 6-cube
Steriruncicantellated 6-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Celliprismatorhombated hexeract (Acronym: coprix) (Jonathan Bowers)
Steriruncicantitruncated 6-cube
Steriuncicantitruncated 6-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Great cellated hexeract (Acronym: gocax) (Jonathan Bowers)
Related polytopes
These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube and 6-orthoplex.
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 Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com,
- (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.