There are 8 unique degrees of runcinations of the 5-cube, along with permutations of truncations and cantellations. Four are more simply constructed relative to the 5-orthoplex.
| bgcolor=#e7dcc3 align=center colspan=3 | Runcinated 5-cube | ||
| Type | Uniform 5-polytope | ||
| Schläfli symbol | t0,3 | ||
| Coxeter diagram | |||
| 4-faces | 202 | 10 80 80 32 | |
| Cells | 1240 | 40 240 320 160 320 160 | |
| Faces | 2160 | 240 960 640 320 | |
| Edges | 1440 | 480+960 | |
| Vertices | 320 | ||
| Vertex figure | |||
| Coxeter group | B5 [4,3,3,3] | ||
| Properties | convex | ||
The Cartesian coordinates of the vertices of a runcinated 5-cube having edge length 2 are all permutations of:
\left(\pm1, \pm1, \pm1, \pm(1+\sqrt{2}), \pm(1+\sqrt{2})\right)
| bgcolor=#e7dcc3 colspan=3 | Runcitruncated 5-cube | ||
|---|---|---|---|
| Type | Uniform 5-polytope | ||
| Schläfli symbol | t0,1,3 | ||
| Coxeter-Dynkin diagrams | |||
| 4-faces | 202 | 10 80 80 32 | |
| Cells | 1560 | 40 240 320 320 160 320 160 | |
| Faces | 3760 | 240 960 320 960 640 640 | |
| Edges | 3360 | 480+960+1920 | |
| Vertices | 960 | ||
| Vertex figure | |||
| Coxeter group | B5, [3,3,3,4] | ||
| Properties | convex | ||
The Cartesian coordinates of the vertices of a runcitruncated 5-cube having edge length 2 are all permutations of:
\left(\pm1, \pm(1+\sqrt{2}), \pm(1+\sqrt{2}), \pm(1+2\sqrt{2}), \pm(1+2\sqrt{2})\right)
| bgcolor=#e7dcc3 align=center colspan=3 | Runcicantellated 5-cube | ||
| Type | Uniform 5-polytope | ||
| Schläfli symbol | t0,2,3 | ||
| Coxeter-Dynkin diagram | |||
| 4-faces | 202 | 10 80 80 32 | |
| Cells | 1240 | 40 240 320 320 160 160 | |
| Faces | 2960 | 240 480 960 320 640 320 | |
| Edges | 2880 | 960+960+960 | |
| Vertices | 960 | ||
| Vertex figure | |||
| Coxeter group | B5 [4,3,3,3] | ||
| Properties | convex | ||
The Cartesian coordinates of the vertices of a runcicantellated 5-cube having edge length 2 are all permutations of:
\left(\pm1, \pm1, \pm(1+\sqrt{2}), \pm(1+2\sqrt{2}), \pm(1+2\sqrt{2})\right)
| bgcolor=#e7dcc3 align=center colspan=3 | Runcicantitruncated 5-cube | |
| Type | Uniform 5-polytope | |
| Schläfli symbol | t0,1,2,3 | |
| Coxeter-Dynkin diagram | ||
| 4-faces | 202 | |
| Cells | 1560 | |
| Faces | 4240 | |
| Edges | 4800 | |
| Vertices | 1920 | |
| Vertex figure | Irregular 5-cell | |
| Coxeter group | B5 [4,3,3,3] | |
| Properties | convex, isogonal | |
The Cartesian coordinates of the vertices of a runcicantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:
\left(1, 1+\sqrt{2}, 1+2\sqrt{2}, 1+3\sqrt{2}, 1+3\sqrt{2}\right)
These polytopes are a part of a set of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.