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. 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:
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,0,\,±\frac12\right).$$

Representations
A dodecahedral prism has the following Coxeter diagrams:


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