5-orthoplex |
Truncated 5-orthoplex |
Bitruncated 5-orthoplex | |
5-cube |
Truncated 5-cube |
Bitruncated 5-cube | |
Orthogonal projections in B_{5} Coxeter plane |
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In five-dimensional geometry, a truncated 5-orthoplex is a convex uniform 5-polytope, being a truncation of the regular 5-orthoplex.
There are 4 unique truncations of the 5-orthoplex. Vertices of the truncation 5-orthoplex are located as pairs on the edge of the 5-orthoplex. Vertices of the bitruncated 5-orthoplex are located on the triangular faces of the 5-orthoplex. The third and fourth truncations are more easily constructed as second and first truncations of the 5-cube.
Truncated 5-orthoplex | ||
---|---|---|
Type | uniform 5-polytope | |
Schläfli symbol | t{3,3,3,4} t{3,3^{1,1}} | |
Coxeter-Dynkin diagrams | | |
4-faces | 42 | 10 32 |
Cells | 240 | 160 80 |
Faces | 400 | 320 80 |
Edges | 280 | 240 40 |
Vertices | 80 | |
Vertex figure | ( )v{3,4} | |
Coxeter groups | B_{5}, [3,3,3,4], order 3840 D_{5}, [3^{2,1,1}], order 1920 | |
Properties | convex |
Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign (4) and coordinate (20) permutations of
The truncated 5-orthoplex is constructed by a truncation operation applied to the 5-orthoplex. All edges are shortened, and two new vertices are added on each original edge.
Coxeter plane | B_{5} | B_{4} / D_{5} | B_{3} / D_{4} / A_{2} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B_{2} | A_{3} | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Bitruncated 5-orthoplex | ||
---|---|---|
Type | uniform 5-polytope | |
Schläfli symbol | 2t{3,3,3,4} 2t{3,3^{1,1}} | |
Coxeter-Dynkin diagrams | | |
4-faces | 42 | 10 32 |
Cells | 280 | 40 160 80 |
Faces | 720 | 320 320 80 |
Edges | 720 | 480 240 |
Vertices | 240 | |
Vertex figure | { }v{4} | |
Coxeter groups | B_{5}, [3,3,3,4], order 3840 D_{5}, [3^{2,1,1}], order 1920 | |
Properties | convex |
The bitruncated 5-orthoplex can tessellate space in the tritruncated 5-cubic honeycomb.
Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign and coordinate permutations of
The bitrunacted 5-orthoplex is constructed by a bitruncation operation applied to the 5-orthoplex.
Coxeter plane | B_{5} | B_{4} / D_{5} | B_{3} / D_{4} / A_{2} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B_{2} | A_{3} | |
Graph | |||
Dihedral symmetry | [4] | [4] |
This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.