57-cell
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| 57-cell | |
|---|---|
| Rank | 4 |
| Type | Regular |
| Notation | |
| Schläfli symbol | |
| Elements | |
| Cells | 57 hemidodecahedra |
| Faces | 171 pentagons |
| Edges | 171 |
| Vertices | 57 |
| Vertex figure | Hemiicosahedron |
| Edge figure | Pentagon |
| Petrie polygons | 190 enneagons |
| Related polytopes | |
| Dual | 57-cell |
| Abstract & topological properties | |
| Flag count | 3420 |
| Euler characteristic | 0 |
| Schläfli type | {5,3,5} |
| Orientable | No |
| Skeleton | Perkel graph |
| Properties | |
| Symmetry | L2(19), order 3420 |
| History | |
| Discovered by | H. S. M. Coxeter |
| First discovered | 1982 |
The 57-cell, or pentacontakaiheptachoron, is a abstract regular polychoron. It has 57 hemidodecahedral cells.
External links[edit | edit source]
- Wikipedia Contributors. "57-cell".
- Weisstein, Eric W. "57-Cell" at MathWorld.
- Klitzing, Richard. "57-cell"
Bibliography[edit | edit source]
- Séquin, Carlo; Hamlin, James (2007). The Regular 4-Dimensional 57-cell (PDF). SIGGRAPH.