57-cell
From Wikipedia, the free encyclopedia
| 57-cell | |
|---|---|
| Type | Abstract regular polychoron |
| Cells | 57 hemi-dodecahedra |
| Faces | 171 {5} |
| Edges | 171 |
| Vertices | 57 |
| Vertex figure | (hemi-icosahedron) |
| Schläfli symbol | {5,3,5} |
| Symmetry group | L2(19) (order 3420) |
| Dual | self-dual |
| Properties | |
In mathematics, the 57-cell (or pentacontaheptachoron) is a self-dual abstract regular polychoron (four-dimensional polytope). Its 57 cells are hemi-dodecahedra. It also has 57 vertices, 171 edges and 171 faces. Its symmetry group is the projective special linear group L2(19), so it has 3420 symmetries.
It has Schläfli symbol {5,3,5} with 5 hemi-dodecahedral cells around each edge. It was discovered by H. S. M. Coxeter in 1982.
[edit] See also
- 11-cell - abstract regular polytope with hemi-icosahedral cells.
- Order-5 dodecahedral honeycomb - regular honeycomb with same Schläfli symbol {5,3,5}.
[edit] References
- Peter McMullen, Egon Schulte, Abstract Regular Polytopes, Cambridge University Press, 2002. ISBN 0-521-81496-0
- [1] PDF The Regular 4-Dimensional 57-Cell, Carlo H. Séquin and James F. Hamlin, CS Division, U.C. Berkeley
