5-orthoplex
In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces.
| Regular 5-orthoplex (pentacross) | |
|---|---|
Orthogonal projection inside Petrie polygon | |
| Type | Regular 5-polytope |
| Family | orthoplex |
| Schläfli symbol | {3,3,3,4} {3,3,31,1} |
| Coxeter-Dynkin diagrams | |
| 4-faces | 32 {33} |
| Cells | 80 {3,3} |
| Faces | 80 {3} |
| Edges | 40 |
| Vertices | 10 |
| Vertex figure | 16-cell |
| Petrie polygon | decagon |
| Coxeter groups | BC5, [3,3,3,4] D5, [32,1,1] |
| Dual | 5-cube |
| Properties | convex, Hanner polytope |
It has two constructed forms, the first being regular with Schläfli symbol {33,4}, and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol {3,3,31,1} or Coxeter symbol 211.
It is a part of an infinite family of polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 5-hypercube or 5-cube.
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