There are 7 truncation for the 8-orthoplex. Vertices of the truncation 8-orthoplex are located as pairs on the edge of the 8-orthoplex. Vertices of the bitruncated 8-orthoplex are located on the triangular faces of the 8-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 8-orthoplex. The final truncations are best expressed relative to the 8-cube.
| bgcolor=#e7dcc3 colspan=2 | Truncated 8-orthoplex | |
|---|---|---|
| Type | uniform 8-polytope | |
| Schläfli symbol | t0,1 | |
| Coxeter-Dynkin diagrams | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 1456 | |
| Vertices | 224 | |
| Vertex figure | v | |
| Coxeter groups | B8, [3,3,3,3,3,3,4] D8, [3<sup>5,1,1</sup>] | |
| Properties | convex |
There are two Coxeter groups associated with the truncated 8-orthoplex, one with the C8 or [4,3,3,3,3,3,3] Coxeter group, and a lower symmetry with the D8 or [3<sup>5,1,1</sup>] Coxeter group.
Cartesian coordinates for the vertices of a truncated 8-orthoplex, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of
(±2,±1,0,0,0,0,0,0)
| bgcolor=#e7dcc3 colspan=2 | Bitruncated 8-orthoplex | |
|---|---|---|
| Type | uniform 8-polytope | |
| Schläfli symbol | t1,2 | |
| Coxeter-Dynkin diagrams | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | ||
| Vertices | ||
| Vertex figure | v | |
| Coxeter groups | B8, [3,3,3,3,3,3,4] D8, [3<sup>5,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of
(±2,±2,±1,0,0,0,0,0)
| bgcolor=#e7dcc3 colspan=2 | Tritruncated 8-orthoplex | |
|---|---|---|
| Type | uniform 8-polytope | |
| Schläfli symbol | t2,3 | |
| Coxeter-Dynkin diagrams | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | ||
| Vertices | ||
| Vertex figure | v | |
| Coxeter groups | B8, [3,3,3,3,3,3,4] D8, [3<sup>5,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of
(±2,±2,±2,±1,0,0,0,0)