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| Regular octaexon (7-simplex) |
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|---|---|
 Orthogonal projection inside Petrie polygon |
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| Type | Regular 7-polytope |
| Family | simplex |
| 6-faces | 8 6-simplex |
| 5-faces | 28 5-simplex |
| 4-faces | 56 5-cell |
| Cells | 70 tetrahedron |
| Faces | 56 triangle |
| Edges | 28 |
| Vertices | 8 |
| Vertex figure | 6-simplex |
| Petrie polygon | octagon |
| Schläfli symbol | {3,3,3,3,3,3} |
| Coxeter-Dynkin diagram |    |
| Coxeter group | A7 [3,3,3,3,3,3] |
| Dual | Self-dual |
| Properties | convex |
An octexon, or octa-7-tope is a 7-simplex, a self-dual regular 7-polytope with 8 vertices, 28 edges, 56 triangle faces, 70 tetrahedral cells, 56 5-cell 5-faces, 28 5-simplex 6-faces, and 8 6-simplex 7-faces.
The name octaexon is derived from octa for eight facets in Greek and -ex for having six-dimensional facets, and -on.
See also
- Other regular 7-polytopes:
- Hepteract - {4,3,3,3,3,3,3}
- Heptacross - {3,3,3,3,3,3,4}
- Others in the simplex family
- Tetrahedron - {3,3}
- 5-cell - {3,3,3}
- 5-simplex - {3,3,3,3}
- 6-simplex - {3,3,3,3,3}
- 7-simplex - {3,3,3,3,3,3}
- 8-simplex - {3,3,3,3,3,3,3}
- 9-simplex - {3,3,3,3,3,3,3,3}
- 10-simplex - {3,3,3,3,3,3,3,3,3}
External links
- Glossary for hyperspace, George Olshevsky.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary
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