11-cell

{| class="wikitable" align="right" style="margin-left:10px" width="250" !bgcolor=#e7dcc3 colspan=2|11-cell |- |bgcolor=#ffffff align=center colspan=2|240pxThe 11 hemi-icosahedra with vertices labeled by indices 0..9,t. Faces are colored by the cell it connects to, defined by the small colored boxes. |- |bgcolor=#e7dcc3|Type||Abstract regular 4-polytope |- |bgcolor=#e7dcc3|Cells||11 hemi-icosahedron150px |- |bgcolor=#e7dcc3|Faces||55 {3} |- |bgcolor=#e7dcc3|Edges||55 |- |bgcolor=#e7dcc3|Vertices||11 |- |bgcolor=#e7dcc3|Vertex figure||hemi-dodecahedron |- |bgcolor=#e7dcc3|Schläfli symbol||\{\{3,5\}_5,\{5,3\}_5\} |- |bgcolor=#e7dcc3|Symmetry group||order 660Abstract L2(11) |- |bgcolor=#e7dcc3|Dual||self-dual |- |bgcolor=#e7dcc3|Properties||Regular |} In mathematics, the 11-cell is a self-dual abstract regular 4-polytope (four-dimensional polytope). Its 11 cells are hemi-icosahedral. It has 11 vertices, 55 edges and 55 faces. It has Schläfli type {3,5,3}, with 3 hemi-icosahedra (Schläfli type {3,5}) 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, .