57-cell
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In mathematics, the 57-cell (pentacontaheptachoron) is a four-dimensional self-dual abstract regular polytope (polychoron). Its 57 facets 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}. 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
