57-cell

57-cell

Some drawings of the Perkel graph.
TypeAbstract regular 4-polytope
Cells57 hemi-dodecahedra
Faces171 {5}
Edges171
Vertices57
Vertex figure(hemi-icosahedron)
Schläfli symbol{5,3,5}
Symmetry groupL2(19) (order 3420)
Dualself-dual
PropertiesRegular

In mathematics, the 57-cell (pentacontakaiheptachoron) is a self-dual abstract regular 4-polytope (four-dimensional polytope). Its 57 cells are hemi-dodecahedra. It also has 57 vertices, 171 edges and 171 two-dimensional 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 (1982).

Perkel graph

The vertices and edges form the Perkel graph, the unique distance-regular graph with intersection array {6,5,2;1,1,3}, discovered by Manley Perkel (1979).

See also

References

External links

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