6-cube |
Cantellated 6-cube |
Bicantellated 6-cube | |||||||||
6-orthoplex |
Cantellated 6-orthoplex |
Bicantellated 6-orthoplex | |||||||||
Cantitruncated 6-cube |
Bicantitruncated 6-cube |
Bicantitruncated 6-orthoplex |
Cantitruncated 6-orthoplex | ||||||||
Orthogonal projections in B6 Coxeter plane |
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In six-dimensional geometry, 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 | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | rr{4,3,3,3,3} or |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 4800 |
Vertices | 960 |
Vertex figure | |
Coxeter groups | B6, [3,3,3,3,4] |
Properties | convex |
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Cantellated 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | 2rr{4,3,3,3,3} or |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B6, [3,3,3,3,4] |
Properties | convex |
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Cantellated 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | tr{4,3,3,3,3} or |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B6, [3,3,3,3,4] |
Properties | convex |
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
It is fourth in a series of cantitruncated hypercubes:
Truncated cuboctahedron | Cantitruncated tesseract | Cantitruncated 5-cube | Cantitruncated 6-cube | Cantitruncated 7-cube | Cantitruncated 8-cube |
Cantellated 6-cube | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | 2tr{4,3,3,3,3} or |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B6, [3,3,3,3,4] |
Properties | convex |
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
These polytopes are part of a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.