5-orthoplex |
Cantellated 5-orthoplex |
Bicantellated 5-cube |
Cantellated 5-cube |
Cantitruncated 5-orthoplex |
Bicantitruncated 5-cube |
Cantitruncated 5-cube |
5-cube |
Orthogonal projections in BC5 Coxeter plane |
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In six-dimensional geometry, a 'cantellated 5-orthoplex is a convex uniform 5-polytope, being a cantellation of the regular 5-orthoplex.
There are 6 cantellation for the 5-orthoplex, including truncations. Some of them are more easily constructed from the dual 5-cube.
Cantellated 5-orthoplex
Cantellated 5-orthoplex | ||
Type | Uniform 5-polytope | |
Schläfli symbol | t0,2{3,3,3,4} t0,2{3,3,31,1} | |
Coxeter-Dynkin diagram | | |
4-faces | 122 | |
Cells | 680 | |
Faces | 1520 | |
Edges | 1280 | |
Vertices | 320 | |
Vertex figure | ||
Coxeter group | BC5 [4,3,3,3] D5 [32,1,1] | |
Properties | convex |
Alternate names
- Cantellated 5-orthoplex
- Bicantellated 5-demicube
- Small rhombated triacontiditeron (Acronym: sart) (Jonathan Bowers)
Coordinates
The vertices of the can be made in 5-space, as permutations and sign combinations of:
- (0,0,1,1,2)
Images
The cantellated 5-orthoplex is constructed by a cantellation operation applied to the 5-orthoplex.
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Cantitruncated 5-orthoplex
Cantitruncated 5-orthoplex | |
---|---|
Type | uniform polyteron |
Schläfli symbol | t0,1,2{3,3,3,4} t0,1,2{3,31,1} |
Coxeter-Dynkin diagrams | |
4-faces | 122 |
Cells | 680 |
Faces | 1520 |
Edges | 1600 |
Vertices | 640 |
Vertex figure | |
Coxeter groups | BC5, [3,3,3,4] D5, [32,1,1] |
Properties | convex |
Alternate names
- Cantitruncated pentacross
- Cantitruncated triacontiditeron (Acronym: gart) (Jonathan Bowers)
Coordinates
Cartesian coordinates for the vertices of a cantitruncated 5-orthoplex, centered at the origin, are all sign and coordinate permutations of
- (±3,±2,±1,0,0)
Images
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Related polytopes
These polytopes are from a set of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.
References
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- Klitzing, Richard. "5D uniform polytopes (polytera)". |x3o3x3o4o - sart, x3x3x3o4o - gart
External links
- Glossary for hyperspace, George Olshevsky.
- Polytopes of Various Dimensions, Jonathan Bowers
- Multi-dimensional Glossary