5-cube |
Runcinated 5-cube |
Runcinated 5-orthoplex |
Runcitruncated 5-cube |
Runcicantellated 5-cube |
Runcicantitruncated 5-cube |
Runcitruncated 5-orthoplex |
Runcicantellated 5-orthoplex |
Runcicantitruncated 5-orthoplex |
Orthogonal projections in BC5 Coxeter plane |
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In five-dimensional geometry, a runcinated 5-cube is a convex uniform 5-polytope that is a runcination (a 3rd order truncation) of the regular 5-cube.
There are unique 8 degrees of runcinations of the 5-cube, along with permutations of truncations, and cantellations. Four are more simply constructed relative to the 5-orthoplex.
|
Runcinated 5-cube | ||
Type | Uniform 5-polytope | |
Schläfli symbol | t0,3{4,3,3,3} | |
Coxeter-Dynkin diagram | ||
4-faces | 162 | |
Cells | 1200 | |
Faces | 2160 | |
Edges | 1440 | |
Vertices | 320 | |
Vertex figure | ||
Coxeter group | BC5 [4,3,3,3] | |
Properties | convex |
The Cartesian coordinates of the vertices of a runcinated 5-cube having edge length 2 are all permutations of:
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Runcitruncated 5-cube | |
---|---|
Type | uniform polyteron |
Schläfli symbol | t0,1,3{4,3,3,3} |
Coxeter-Dynkin diagrams | |
4-faces | 162 |
Cells | 1440 |
Faces | 3680 |
Edges | 3360 |
Vertices | 960 |
Vertex figure | |
Coxeter groups | BC5, [3,3,3,4] |
Properties | convex |
The Cartesian coordinates of the vertices of a truncated 5-cube having edge length 2 are all permutations of:
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Runcicantellated 5-cube | ||
Type | Uniform 5-polytope | |
Schläfli symbol | t0,2,3{4,3,3,3} | |
Coxeter-Dynkin diagram | ||
4-faces | 162 | |
Cells | 1200 | |
Faces | 2960 | |
Edges | 2880 | |
Vertices | 960 | |
Vertex figure | ||
Coxeter group | BC5 [4,3,3,3] | |
Properties | convex |
The Cartesian coordinates of the vertices of a runcicantellated 5-cube having edge length 2 are all permutations of:
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Runcicantitruncated 5-cube | ||
Type | Uniform 5-polytope | |
Schläfli symbol | t0,1,2,3{4,3,3,3} | |
Coxeter-Dynkin diagram |
||
4-faces | 162 | |
Cells | 1440 | |
Faces | 4160 | |
Edges | 4800 | |
Vertices | 1920 | |
Vertex figure | ||
Coxeter group | BC5 [4,3,3,3] | |
Properties | convex, isogonal |
The Cartesian coordinates of the vertices of an runcicantitruncated tesseract having an edge length of 2 are given by all permutations of coordinates and sign of:
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
These polytopes are a part of a set of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.