11-cell

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In mathematics, the 11-cell (hendecachoron) is a four-dimensional self-dual abstract regular polytope (polychoron). Its 11 facets are hemi-icosahedral. It also has 11 vertices, 55 edges and 55 faces. Its symmetry group is the projective special linear group L₂(11), so it has 660 symmetries. It has Schläfli symbol {3,5,3}.

It was discovered by Branko Grünbaum in 1977, who constructed it by pasting hemi-icosahedra together, three per edge until the shape closed up. It was independently discovered by H. S. M. Coxeter in 1984, who studied its structure and symmetry in greater depth.

[edit] See also

• 57-cell
• Order-3 icosahedral honeycomb - regular honeycomb with same Schläfli symbol {3,5,3}.

[edit] References

• Peter McMullen, Egon Schulte, Abstract Regular Polytopes, Cambridge University Press, 2002. ISBN 0-521-81496-0