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.
| bgcolor=#e7dcc3 colspan=3 | Truncated 5-orthoplex | ||
|---|---|---|---|
| Type | uniform 5-polytope | ||
| Schläfli symbol | t t | ||
| 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 | ||
| Coxeter groups | B5, [3,3,3,4], order 3840 D5, [3<sup>2,1,1</sup>], 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
(±2,±1,0,0,0)
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.
| bgcolor=#e7dcc3 colspan=3 | Bitruncated 5-orthoplex | ||
|---|---|---|---|
| Type | uniform 5-polytope | ||
| Schläfli symbol | 2t 2t | ||
| 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 | ||
| Coxeter groups | B5, [3,3,3,4], order 3840 D5, [3<sup>2,1,1</sup>], order 1920 | ||
| Properties | convex | ||
Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign and coordinate permutations of
(±2,±2,±1,0,0)
The bitrunacted 5-orthoplex is constructed by a bitruncation operation applied to the 5-orthoplex.
This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.