Rectified 5-cell
From Wikipedia, the free encyclopedia
| Rectified 5-cell | |
|---|---|
 stereographic projection (centered on octahedron) |
|
| Type | Uniform polychoron |
| Cells | 5 (3.3.3) 5 (3.3.3.3) |
| Faces | 30 {3} |
| Edges | 30 |
| Vertices | 10 |
| Vertex figure | 2 (3.3.3) 3 (3.3.3.3) (triangular prism) |
| Schläfli symbol | t1{3,3,3} |
| Symmetry group | A4, [3,3,3] |
| Properties | convex |
In geometry, the rectified 5-cell is a uniform polychoron composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge has one tetrahedron and two octahedra. Each vertex has two tetrahedra and three octahedra. In total it has 30 triangle faces, 30 edges, and 10 vertices.
It is one of three semiregular polychora made of two or more cells which are platonic solids.
Names:
- Dispentachoron
- Rectified 5-cell (Norman W. Johnson)
- Rectified pentachoron
- Rectified 4-simplex
- Rap (Jonathan Bowers: for rectified pentachoron)
- Ambopentachoron (Neil Sloane & John Horton Conway)
The vertex figure of the 10-cell is a uniform triangular prism.
[edit] See also
[edit] External links
- Rectified 5-cell - data and images
- Convex uniform polychora based on the pentachoron (5-cell), George Olshevsky (2)
