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In seven-dimensional geometry, a cantellated 7-orthoplex is a convex uniform 7-polytope, being a cantellation of the regular 7-orthoplex.
7-orthoplex |
Cantellated 7-orthoplex |
Bicantellated 7-orthoplex |
Birectified 7-orthoplex |
Cantitruncated 7-orthoplex |
Bicantitruncated 7-orthoplex |
Cantellated 7-cube |
Bicantellated 7-cube |
Tricantellated 7-cube |
Cantitruncated 7-cube |
Bicantitruncated 7-cube |
Tricantitruncated 7-cube |
Orthogonal projections in B6 Coxeter plane |
---|
There are ten degrees of cantellation for the 7-orthoplex, including truncations. Six are most simply constructible from the dual 7-cube.
Cantellated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | rr{3,3,3,3,3,4} |
Coxeter-Dynkin diagram | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 7560 |
Vertices | 840 |
Vertex figure | |
Coxeter groups | B7, [4,3,3,3,3,3] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Bicantellated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | 2rr{3,3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter groups | B7, [4,3,3,3,3,3] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Cantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | tr{3,3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 8400 |
Vertices | 1680 |
Vertex figure | |
Coxeter groups | B7, [4,3,3,3,3,3] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | too complex | ||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Bicantitruncated 7-orthoplex | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | 2tr{3,3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 30240 |
Vertices | 6720 |
Vertex figure | |
Coxeter groups | B7, [4,3,3,3,3,3] |
Properties | convex |
Coxeter plane | B7 / A6 | B6 / D7 | B5 / D6 / A4 |
---|---|---|---|
Graph | too complex | ||
Dihedral symmetry | [14] | [12] | [10] |
Coxeter plane | B4 / D5 | B3 / D4 / A2 | B2 / D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
These polytopes are from a family of 127 uniform 7-polytopes with B7 symmetry.
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