Decagonal-dodecahedral duoprism

The decagonal-dodecahedral duoprism or dadoe is a convex uniform duoprism that consists of 10 dodecahedral prisms and 12 pentagonal-decagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal-decagonal duoprisms.

Vertex coordinates
The vertices of a decagonal-dodecahedral duoprism of edge length 1 are given by: as well as all even permutations of the last three coordinates of:
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4}\right).$$

Representations
A decagonal-dodecahedral duoprism has the following Coxeter diagrams:
 * x10o x5o3o (full symmetry)
 * x5x x5o3o (decagons as dipentagons)