Dodecahedral prism

The dodecahedral prism or dope is a prismatic uniform polychoron that consists of 2 dodecahedra and 12 pentagonal prisms. Each vertex joins 1 dodecahedron and 3 pentagonal prisms. As the name suggests, it is a prism based on the dodecahedron. As such it is also a convex segmentochoron (designated K-4.74 on Richard Klitzing's list).

Vertex coordinates
The vertices of a dodecahedral prism of edge length 1 are given by all permutations and changes of sign of the first three coordinates of: along with all even permutations and all sign changes of:
 * (±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{2}$)/4, ±(1+$\sqrt{(11+3√5)/8}$)/4, ±1/2),
 * (±(3+$\sqrt{5}$)/4, ±1/2, 0, ±1/2).

Representations
A dodecahedral prism has the following Coxeter diagrams:


 * x x5o3o (full symmetry)
 * xx5oo3oo&#x (cases considered separately)