| bgcolor=#e7dcc3 colspan=2 | Truncated 5-demicube Cantic 5-cube | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | D5 Coxeter plane projection | |
| Type | uniform 5-polytope | |
| Schläfli symbol | h2 t | |
| Coxeter-Dynkin diagram | = | |
| 4-faces | 42 total: 16 r 16 t 10 t | |
| Cells | 280 total: 80 120 t 80 | |
| Faces | 640 total: 480 160 | |
| Edges | 560 | |
| Vertices | 160 | |
| Vertex figure | v× | |
| Coxeter groups | D5, [3<sup>2,1,1</sup>] | |
| Properties | convex |
The Cartesian coordinates for the 160 vertices of a cantic 5-cube centered at the origin and edge length 6 are coordinate permutations:
(±1,±1,±3,±3,±3)with an odd number of plus signs.
It has half the vertices of the cantellated 5-cube, as compared here in the B5 Coxeter plane projections:
This polytope is based on the 5-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 23 uniform 5-polytope that can be constructed from the D5 symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family.