There are 6 truncations for the 7-cube. Vertices of the truncated 7-cube are located as pairs on the edge of the 7-cube. Vertices of the bitruncated 7-cube are located on the square faces of the 7-cube. Vertices of the tritruncated 7-cube are located inside the cubic cells of the 7-cube. The final three truncations are best expressed relative to the 7-orthoplex.
| bgcolor=#e7dcc3 colspan=2 | Truncated 7-cube | |
|---|---|---|
| Type | uniform 7-polytope | |
| Schläfli symbol | t | |
| Coxeter-Dynkin diagrams | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 3136 | |
| Vertices | 896 | |
| Vertex figure | Elongated 5-simplex pyramid | |
| Coxeter groups | B7, [3<sup>5</sup>,4] | |
| Properties | convex |
Cartesian coordinates for the vertices of a truncated 7-cube, centered at the origin, are all sign and coordinate permutations of
(1,1+√2,1+√2,1+√2,1+√2,1+√2,1+√2)
The truncated 7-cube, is sixth in a sequence of truncated hypercubes:
| bgcolor=#e7dcc3 colspan=2 | Bitruncated 7-cube | |
|---|---|---|
| Type | uniform 7-polytope | |
| Schläfli symbol | 2t | |
| Coxeter-Dynkin diagrams | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 9408 | |
| Vertices | 2688 | |
| Vertex figure | v | |
| Coxeter groups | B7, [3<sup>5</sup>,4] D7, [3<sup>4,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a bitruncated 7-cube, centered at the origin, are all sign and coordinate permutations of
(±2,±2,±2,±2,±2,±1,0)
The bitruncated 7-cube is fifth in a sequence of bitruncated hypercubes:
| bgcolor=#e7dcc3 colspan=2 | Tritruncated 7-cube | |
|---|---|---|
| Type | uniform 7-polytope | |
| Schläfli symbol | 3t | |
| Coxeter-Dynkin diagrams | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 13440 | |
| Vertices | 3360 | |
| Vertex figure | v | |
| Coxeter groups | B7, [3<sup>5</sup>,4] D7, [3<sup>4,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a tritruncated 7-cube, centered at the origin, are all sign and coordinate permutations of
(±2,±2,±2,±2,±1,0,0)