7-cube |
Rectified 7-cube |
Birectified 7-cube |
Trirectified 7-cube |
Birectified 7-orthoplex |
Rectified 7-orthoplex |
7-orthoplex |
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Orthogonal projections in BC7 Coxeter plane |
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In seven-dimensional geometry, a rectified 7-cube is a convex uniform 7-polytope, being a rectification of the regular 7-cube.
There are unique 7 degrees of rectifications, the zeroth being the 7-cube, and the 6th and last being the 7-cube. Vertices of the rectified 7-cube are located at the edge-centers of the 7-ocube. Vertices of the birectified 7-cube are located in the square face centers of the 7-cube. Vertices of the trirectified 7-cube are located in the cube cell centers of the 7-cube.
Contents |
Rectified 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t1{4,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | 5-simplex prism |
Coxeter groups | BC7, [3,3,3,3,3,4] |
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] |
Cartesian coordinates for the vertices of a rectified 7-cube, centered at the origin, edge length are all permutations of:
Birectified 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t2{4,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | {3}x{3,3,3} |
Coxeter groups | BC7, [3,3,3,3,3,4] |
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] |
Cartesian coordinates for the vertices of a birectified 7-cube, centered at the origin, edge length are all permutations of:
Trirectified 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t3{4,3,3,3,3,3} |
Coxeter-Dynkin diagrams | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | {3,3}x{3,3} |
Coxeter groups | BC7, [3,3,3,3,3,4] |
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] |
Cartesian coordinates for the vertices of a trirectified 7-cube, centered at the origin, edge length are all permutations of: