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In five-dimensional geometry, a cantellated 5-orthoplex is a convex uniform 5-polytope, being a cantellation of the regular 5-orthoplex.
![]() 5-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Cantellated 5-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bicantellated 5-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Cantellated 5-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() 5-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Cantitruncated 5-orthoplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bicantitruncated 5-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Cantitruncated 5-cube ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Orthogonal projections in B5 Coxeter plane |
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There are 6 cantellation for the 5-orthoplex, including truncations. Some of them are more easily constructed from the dual 5-cube.
Cantellated 5-orthoplex | ||
Type | Uniform 5-polytope | |
Schläfli symbol | rr{3,3,3,4} rr{3,3,31,1} | |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4-faces | 82 | 10 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 40 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 32 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 640 | 80 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() |
Faces | 1520 | 640 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() 480 ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() |
Edges | 1200 | 960 ![]() 240 ![]() |
Vertices | 240 | |
Vertex figure | Square pyramidal prism ![]() | |
Coxeter group | B5, [4,3,3,3], order 3840 D5, [32,1,1], order 1920 | |
Properties | convex |
The vertices of the can be made in 5-space, as permutations and sign combinations of:
The cantellated 5-orthoplex is constructed by a cantellation operation applied to the 5-orthoplex.
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | ![]() |
![]() |
![]() |
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | ![]() |
![]() | |
Dihedral symmetry | [4] | [4] |
Cantitruncated 5-orthoplex | ||
---|---|---|
Type | uniform 5-polytope | |
Schläfli symbol | tr{3,3,3,4} tr{3,31,1} | |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4-faces | 82 | 10 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 40 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 32 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 640 | 80 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() ![]() ![]() |
Faces | 1520 | 640 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() 480 ![]() ![]() ![]() ![]() 80 ![]() ![]() ![]() ![]() |
Edges | 1440 | 960 ![]() 240 ![]() 240 ![]() |
Vertices | 480 | |
Vertex figure | Square pyramidal pyramid ![]() | |
Coxeter groups | B5, [3,3,3,4], order 3840 D5, [32,1,1], order 1920 | |
Properties | convex |
Cartesian coordinates for the vertices of a cantitruncated 5-orthoplex, centered at the origin, are all sign and coordinate 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] |
These polytopes are from a set of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.
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