11-cell

In mathematics, the 11-cell is a self-dual abstract regular 4-polytope (four-dimensional polytope).

The symmetry structure is the abstract group projective special linear group of the 2-dimensional vector space over the finite field with 11 elements L2(11).

It was discovered in 1977 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.

Thus it can be drawn as a regular figure in 10-space, although then its hemi-icosahedral cells are skew; that is, each cell is not contained within a flat 3-dimensional subspace.