9-orthoplex
| Regular 9-orthoplex Enneacross | |
|---|---|
Orthogonal projection inside Petrie polygon | |
| Type | Regular 9-polytope |
| Family | orthoplex |
| Schläfli symbol | {37,4} {36,31,1} |
| Coxeter-Dynkin diagrams | |
| 8-faces | 512 {37} |
| 7-faces | 2304 {36} |
| 6-faces | 4608 {35} |
| 5-faces | 5376 {34} |
| 4-faces | 4032 {33} |
| Cells | 2016 {3,3} |
| Faces | 672 {3} |
| Edges | 144 |
| Vertices | 18 |
| Vertex figure | Octacross |
| Petrie polygon | Octadecagon |
| Coxeter groups | C9, [37,4] D9, [36,1,1] |
| Dual | 9-cube |
| Properties | convex, Hanner polytope |
In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032 5-cell 4-faces, 5376 5-simplex 5-faces, 4608 6-simplex 6-faces, 2304 7-simplex 7-faces, and 512 8-simplex 8-faces.
It has two constructed forms, the first being regular with Schläfli symbol {37,4}, and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol h{36,31,1} or Coxeter symbol 611t.
It is one of an infinite family of /polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 9-hypercube or enneract.*