Cantellated 6-cube
Encyclopedia
6-cube |
Cantellated 6-cube |
Bicantellated 6-cube |
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6-orthoplex |
Cantellated 6-orthoplex Cantellated 6-orthoplex In six-dimensional geometry, a cantellated 6-orthoplex is a convex uniform 6-polytope, being a cantellation of the regular 6-orthoplex.There are 8 cantellation for the 6-orthoplex including truncations... |
Bicantellated 6-orthoplex |
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Cantitruncated 6-cube |
Bicantitruncated 6-cube |
Bicantitruncated 6-orthoplex |
Cantitruncated 6-orthoplex |
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| Orthogonal projections in BC6 Coxeter plane | |||||||||||
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In six-dimensional geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a cantellated 6-cube is a convex uniform 6-polytope, being a cantellation of the regular 6-cube.
There are 8 cantellations for the 6-cube, including truncations. Half of them are more easily constructed from the dual 5-orthoplex
Cantellated 6-cube
| Cantellated 6-cube | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,2{4,3,3,3,3} |
| Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... s |
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| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 4800 |
| Vertices | 960 |
| Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:... |
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| Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... s |
B6, [3,3,3,3,4] |
| Properties | convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn... |
Alternate names
- Cantellated hexeract
- Small rhombated hexeract (acronym: srox) (Jonathan Bowers)
Alternate names
- Bicantellated hexeract
- Small birhombated hexeract (acronym: saborx) (Jonathan Bowers)
Alternate names
- Cantitruncated hexeract
- Great rhombihexeract (acronym: grox) (Jonathan Bowers)
Alternate names
- Bicantitruncated hexeract
- Great birhombihexeract (acronym: gaborx) (Jonathan Bowers)