There are unique 7 degrees of truncation for the 8-cube. Vertices of the truncation 8-cube are located as pairs on the edge of the 8-cube. Vertices of the bitruncated 8-cube are located on the square faces of the 8-cube. Vertices of the tritruncated 7-cube are located inside the cubic cells of the 8-cube. The final truncations are best expressed relative to the 8-orthoplex.
| bgcolor=#e7dcc3 colspan=2 | Truncated 8-cube | |
|---|---|---|
| Type | uniform 8-polytope | |
| Schläfli symbol | t | |
| 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] | |
| Properties | convex |
Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of
(±2,±2,±2,±2,±2,±2,±1,0)
The truncated 8-cube, is seventh in a sequence of truncated hypercubes:
| bgcolor=#e7dcc3 colspan=2 | Bitruncated 8-cube | |
|---|---|---|
| Type | uniform 8-polytope | |
| Schläfli symbol | 2t | |
| 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] | |
| Properties | convex |
Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of
(±2,±2,±2,±2,±2,±1,0,0)
The bitruncated 8-cube is sixth in a sequence of bitruncated hypercubes:
| bgcolor=#e7dcc3 colspan=2 | Tritruncated 8-cube | |
|---|---|---|
| Type | uniform 8-polytope | |
| Schläfli symbol | 3t | |
| 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] | |
| Properties | convex |
Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of
(±2,±2,±2,±2,±1,0,0,0)
| bgcolor=#e7dcc3 colspan=2 | Quadritruncated 8-cube | |
|---|---|---|
| Type | uniform 8-polytope | |
| Schläfli symbol | 4t | |
| 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,±2,±1,0,0,0)