The 600-Cell

The 600-cell is composed of 600 tetrahedra, joined 5 to an edge. It has 120 vertices. It is the dual of the 120-cell.

It is the 4D equivalent of the icosahedron, just as the 120-cell is the 4D equivalent of the dodecahedron. Its vertex figure is an icosahedron. Twenty tetrahedral cells meet at every vertex, in an icosahedral arrangement. The faces of these tetrahedra opposite the central vertex form the faces of an icosahedron.