There are 9 rectifications of the 9-orthoplex. Vertices of the rectified 9-orthoplex are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 9-orthoplex are located in the triangular face centers of the 9-orthoplex. Vertices of the trirectified 9-orthoplex are located in the tetrahedral cell centers of the 9-orthoplex.
These polytopes are part of a family 511 uniform 9-polytopes with BC9 symmetry.
| bgcolor=#e7dcc3 colspan=2 | Rectified 9-orthoplex | |
|---|---|---|
| Type | uniform 9-polytope | |
| Schläfli symbol | t1 | |
| Coxeter-Dynkin diagrams | ||
| 7-faces | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 2016 | |
| Vertices | 144 | |
| Vertex figure | 7-orthoplex prism | |
| Petrie polygon | octakaidecagon | |
| Coxeter groups | C9, [4,3<sup>7</sup>] D9, [3<sup>6,1,1</sup>] | |
| Properties | convex |
The rectified 9-orthoplex is the vertex figure for the demienneractic honeycomb.
or
There are two Coxeter groups associated with the rectified 9-orthoplex, one with the C9 or [4,3<sup>7</sup>] Coxeter group, and a lower symmetry with two copies of 8-orthoplex facets, alternating, with the D9 or [3<sup>6,1,1</sup>] Coxeter group.
Cartesian coordinates for the vertices of a rectified 9-orthoplex, centered at the origin, edge length
\sqrt{2}
(±1,±1,0,0,0,0,0,0,0)
Its 144 vertices represent the root vectors of the simple Lie group D9. The vertices can be seen in 3 hyperplanes, with the 36 vertices rectified 8-simplexs cells on opposite sides, and 72 vertices of an expanded 8-simplex passing through the center. When combined with the 18 vertices of the 9-orthoplex, these vertices represent the 162 root vectors of the B9 and C9 simple Lie groups.