There are 10 rectifications of the 10-cube, with the zeroth being the 10-cube itself. Vertices of the rectified 10-cube are located at the edge-centers of the 10-cube. Vertices of the birectified 10-cube are located in the square face centers of the 10-cube. Vertices of the trirectified 10-cube are located in the cubic cell centers of the 10-cube. The others are more simply constructed relative to the 10-cube dual polytope, the 10-orthoplex.
These polytopes are part of a family 1023 uniform 10-polytopes with BC10 symmetry.
| bgcolor=#e7dcc3 colspan=2 | Rectified 10-orthoplex | |
|---|---|---|
| Type | uniform 10-polytope | |
| Schläfli symbol | t1 | |
| Coxeter-Dynkin diagrams | ||
| 7-faces | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 46080 | |
| Vertices | 5120 | |
| Vertex figure | 8-simplex prism | |
| Coxeter groups | C10, [4,3<sup>8</sup>] D10, [3<sup>7,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a rectified 10-cube, centered at the origin, edge length
\sqrt{2}
(±1,±1,±1,±1,±1,±1,±1,±1,±1,0)
| bgcolor=#e7dcc3 colspan=2 | Birectified 10-orthoplex | |
|---|---|---|
| Type | uniform 10-polytope | |
| Coxeter symbol | 0711 | |
| Schläfli symbol | t2 | |
| Coxeter-Dynkin diagrams | ||
| 7-faces | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 184320 | |
| Vertices | 11520 | |
| Vertex figure | x | |
| Coxeter groups | C10, [4,3<sup>8</sup>] D10, [3<sup>7,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a birectified 10-cube, centered at the origin, edge length
\sqrt{2}
(±1,±1,±1,±1,±1,±1,±1,±1,0,0)
| bgcolor=#e7dcc3 colspan=2 | Trirectified 10-orthoplex | |
|---|---|---|
| Type | uniform 10-polytope | |
| Schläfli symbol | t3 | |
| Coxeter-Dynkin diagrams | ||
| 7-faces | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 322560 | |
| Vertices | 15360 | |
| Vertex figure | x | |
| Coxeter groups | C10, [4,3<sup>8</sup>] D10, [3<sup>7,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a triirectified 10-cube, centered at the origin, edge length
\sqrt{2}
(±1,±1,±1,±1,±1,±1,±1,0,0,0)
| bgcolor=#e7dcc3 colspan=2 | Quadrirectified 10-orthoplex | |
|---|---|---|
| Type | uniform 10-polytope | |
| Schläfli symbol | t4 | |
| Coxeter-Dynkin diagrams | ||
| 7-faces | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 322560 | |
| Vertices | 13440 | |
| Vertex figure | x | |
| Coxeter groups | C10, [4,3<sup>8</sup>] D10, [3<sup>7,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a quadrirectified 10-cube, centered at the origin, edge length
\sqrt{2}
(±1,±1,±1,±1,±1,±1,0,0,0,0)