57-cell

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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

[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

[edit] External links

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