9-simplex
In geometry, a 9-simplex is a self-dual regular 9-polytope. It has 10 vertices, 45 edges, 120 triangle faces, 210 tetrahedral cells, 252 5-cell 4-faces, 210 5-simplex 5-faces, 120 6-simplex 6-faces, 45 7-simplex 7-faces, and 10 8-simplex 8-faces. Its dihedral angle is cos−1(1/9), or approximately 83.62°.
| Regular decayotton (9-simplex) | |
|---|---|
Orthogonal projection inside Petrie polygon | |
| Type | Regular 9-polytope |
| Family | simplex |
| Schläfli symbol | {3,3,3,3,3,3,3,3} |
| Coxeter-Dynkin diagram | |
| 8-faces | 10 8-simplex |
| 7-faces | 45 7-simplex |
| 6-faces | 120 6-simplex |
| 5-faces | 210 5-simplex |
| 4-faces | 252 5-cell |
| Cells | 210 tetrahedron |
| Faces | 120 triangle |
| Edges | 45 |
| Vertices | 10 |
| Vertex figure | 8-simplex |
| Petrie polygon | decagon |
| Coxeter group | A9 [3,3,3,3,3,3,3,3] |
| Dual | Self-dual |
| Properties | convex |
It can also be called a decayotton, or deca-9-tope, as a 10-facetted polytope in 9-dimensions.. The name decayotton is derived from deca for ten facets in Greek and yotta (a variation of "oct" for eight), having 8-dimensional facets, and -on.
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