6-orthoplex
In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell 4-faces, and 64 5-faces.
| 6-orthoplex Hexacross | |
|---|---|
Orthogonal projection inside Petrie polygon | |
| Type | Regular 6-polytope |
| Family | orthoplex |
| Schläfli symbols | {3,3,3,3,4} {3,3,3,31,1} |
| Coxeter-Dynkin diagrams | = |
| 5-faces | 64 {34} |
| 4-faces | 192 {33} |
| Cells | 240 {3,3} |
| Faces | 160 {3} |
| Edges | 60 |
| Vertices | 12 |
| Vertex figure | 5-orthoplex |
| Petrie polygon | dodecagon |
| Coxeter groups | B6, [4,34] D6, [33,1,1] |
| Dual | 6-cube |
| Properties | convex, Hanner polytope |
It has two constructed forms, the first being regular with Schläfli symbol {34,4}, and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol {3,3,3,31,1} or Coxeter symbol 311.
It is a part of an infinite family of polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 6-hypercube, or hexeract.
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