Icosahedral prism

The icosahedral prism or ipe is a prismatic uniform polychoron that consists of 2 icosahedra and 20 triangular prisms. Each vertex joins 1 icosahedron and 5 triangular prisms. As the name suggests, it is a prism based on the icosahedron.

Vertex coordinates
The vertices of a icosahedral prism of edge length 1 are given by all even permutations and all sign changes of the first three coordinates of:
 * (0, 1/2, (1+$\sqrt{2}$)/4, ±1/2)