11-cell
In mathematics, the 11-cell is a self-dual abstract regular 4-polytope. Its 11 cells are hemi-icosahedral. It has 11 vertices, 55 edges and 55 faces. It has Schläfli type, with 3 hemi-icosahedra around each edge.
Its automorphism group has 660 elements. The automorphism group is isomorphic to the projective special linear group of the 2-dimensional vector space over the finite field with 11 elements,.
It was discovered in 1976 by Branko Grünbaum, who constructed it by pasting hemi-icosahedra together, three at each 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. It has since been studied and illustrated by Carlo H. Séquin.
Looking only at the vertices and cells, its abstract structure is geometric configuration and can be defined with a cyclic configuration, with a generator "line" as 11.