There are 5 truncations for the 6-cube. Vertices of the truncated 6-cube are located as pairs on the edge of the 6-cube. Vertices of the bitruncated 6-cube are located on the square faces of the 6-cube. Vertices of the tritruncated 6-cube are located inside the cubic cells of the 6-cube.
| bgcolor=#e7dcc3 colspan=2 | Truncated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Class | B6 polytope | |
| Schläfli symbol | t | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | 76 | |
| 4-faces | 464 | |
| Cells | 1120 | |
| Faces | 1520 | |
| Edges | 1152 | |
| Vertices | 384 | |
| Vertex figure | v | |
| Coxeter groups | B6, [3,3,3,3,4] | |
| Properties | convex |
The truncated 6-cube may be constructed by truncating the vertices of the 6-cube at
1/(\sqrt{2}+2)
The Cartesian coordinates of the vertices of a truncated 6-cube having edge length 2 are the permutations of:
\left(\pm1, \pm(1+\sqrt{2}), \pm(1+\sqrt{2}), \pm(1+\sqrt{2}), \pm(1+\sqrt{2}), \pm(1+\sqrt{2})\right)
The truncated 6-cube, is fifth in a sequence of truncated hypercubes:
| bgcolor=#e7dcc3 colspan=2 | Bitruncated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Class | B6 polytope | |
| Schläfli symbol | 2t | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | ||
| Vertices | ||
| Vertex figure | v | |
| Coxeter groups | B6, [3,3,3,3,4] | |
| Properties | convex |
The Cartesian coordinates of the vertices of a bitruncated 6-cube having edge length 2 are the permutations of:
\left(0, \pm1, \pm2, \pm2, \pm2, \pm2\right)
The bitruncated 6-cube is fourth in a sequence of bitruncated hypercubes:
| bgcolor=#e7dcc3 colspan=2 | Tritruncated 6-cube | |
|---|---|---|
| Type | uniform 6-polytope | |
| Class | B6 polytope | |
| Schläfli symbol | 3t | |
| Coxeter-Dynkin diagrams | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | ||
| Vertices | ||
| Vertex figure | v[3] | |
| Coxeter groups | B6, [3,3,3,3,4] | |
| Properties | convex |
The Cartesian coordinates of the vertices of a tritruncated 6-cube having edge length 2 are the permutations of:
\left(0, 0, \pm1, \pm2, \pm2, \pm2\right)
These polytopes are from a set of 63 Uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.