8-orthoplex
In geometry, an 8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells 4-faces, 1792 5-faces, 1024 6-faces, and 256 7-faces.
| 8-orthoplex Octacross | |
|---|---|
Orthogonal projection inside Petrie polygon | |
| Type | Regular 8-polytope |
| Family | orthoplex |
| Schläfli symbol | {36,4} {3,3,3,3,3,31,1} |
| Coxeter-Dynkin diagrams | |
| 7-faces | 256 {36} |
| 6-faces | 1024 {35} |
| 5-faces | 1792 {34} |
| 4-faces | 1792 {33} |
| Cells | 1120 {3,3} |
| Faces | 448 {3} |
| Edges | 112 |
| Vertices | 16 |
| Vertex figure | 7-orthoplex |
| Petrie polygon | hexadecagon |
| Coxeter groups | C8, [36,4] D8, [35,1,1] |
| Dual | 8-cube |
| Properties | convex, Hanner polytope |
It has two constructive forms, the first being regular with Schläfli symbol {36,4}, and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol {3,3,3,3,3,31,1} or Coxeter symbol 511.
It is a part of an infinite family of polytopes, called cross-polytopes or orthoplexes. The dual polytope is an 8-hypercube, or octeract.
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