![]() 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 B5 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 8 unique 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 diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4-faces | 202 | 10 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 32 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 1240 | 40 ![]() ![]() ![]() ![]() ![]() ![]() 240 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() |
Faces | 2160 | 240 ![]() ![]() ![]() ![]() 960 ![]() ![]() ![]() ![]() 640 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() |
Edges | 1440 | 480+960 |
Vertices | 320 | |
Vertex figure |
![]() | |
Coxeter group | B5 [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 5-polytope | |
Schläfli symbol | t0,1,3{4,3,3,3} | |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4-faces | 202 | 10 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 32 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 1560 | 40 ![]() ![]() ![]() ![]() ![]() ![]() 240 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() |
Faces | 3760 | 240 ![]() ![]() ![]() ![]() 960 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() 960 ![]() ![]() ![]() ![]() 640 ![]() ![]() ![]() ![]() 640 ![]() ![]() ![]() ![]() |
Edges | 3360 | 480+960+1920 |
Vertices | 960 | |
Vertex figure |
![]() | |
Coxeter group | B5, [3,3,3,4] | |
Properties | convex |
The Cartesian coordinates of the vertices of a runcitruncated 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 | 202 | 10 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 32 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 1240 | 40 ![]() ![]() ![]() ![]() ![]() ![]() 240 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() |
Faces | 2960 | 240 ![]() ![]() ![]() ![]() 480 ![]() ![]() ![]() ![]() 960 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() 640 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() |
Edges | 2880 | 960+960+960 |
Vertices | 960 | |
Vertex figure |
![]() | |
Coxeter group | B5 [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 | 202 | |
Cells | 1560 | |
Faces | 4240 | |
Edges | 4800 | |
Vertices | 1920 | |
Vertex figure |
![]() Irregular 5-cell | |
Coxeter group | B5 [4,3,3,3] | |
Properties | convex, isogonal |
The Cartesian coordinates of the vertices of a runcicantitruncated 5-cube 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.
![]() 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 B5 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 8 unique 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 diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4-faces | 202 | 10 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 32 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 1240 | 40 ![]() ![]() ![]() ![]() ![]() ![]() 240 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() |
Faces | 2160 | 240 ![]() ![]() ![]() ![]() 960 ![]() ![]() ![]() ![]() 640 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() |
Edges | 1440 | 480+960 |
Vertices | 320 | |
Vertex figure |
![]() | |
Coxeter group | B5 [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 5-polytope | |
Schläfli symbol | t0,1,3{4,3,3,3} | |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4-faces | 202 | 10 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 32 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 1560 | 40 ![]() ![]() ![]() ![]() ![]() ![]() 240 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() |
Faces | 3760 | 240 ![]() ![]() ![]() ![]() 960 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() 960 ![]() ![]() ![]() ![]() 640 ![]() ![]() ![]() ![]() 640 ![]() ![]() ![]() ![]() |
Edges | 3360 | 480+960+1920 |
Vertices | 960 | |
Vertex figure |
![]() | |
Coxeter group | B5, [3,3,3,4] | |
Properties | convex |
The Cartesian coordinates of the vertices of a runcitruncated 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 | 202 | 10 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 32 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 1240 | 40 ![]() ![]() ![]() ![]() ![]() ![]() 240 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() |
Faces | 2960 | 240 ![]() ![]() ![]() ![]() 480 ![]() ![]() ![]() ![]() 960 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() 640 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() |
Edges | 2880 | 960+960+960 |
Vertices | 960 | |
Vertex figure |
![]() | |
Coxeter group | B5 [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 | 202 | |
Cells | 1560 | |
Faces | 4240 | |
Edges | 4800 | |
Vertices | 1920 | |
Vertex figure |
![]() Irregular 5-cell | |
Coxeter group | B5 [4,3,3,3] | |
Properties | convex, isogonal |
The Cartesian coordinates of the vertices of a runcicantitruncated 5-cube 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.