Hexagonal-dodecahedral duoprism

The hexagonal-dodecahedral duoprism or hadoe is a convex uniform duoprism that consists of 6 dodecahedral prisms and 12 pentagonal-hexagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal-hexagonal duoprisms.

Vertex coordinates
The vertices of a hexagonal-dodecahedral duoprism of edge length 1 are given by: as well as all even permutations of the last three coordinates of:
 * $$\left(0,\,±1,\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(0,\,±1,\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4}\right).$$

Representations
A hexagonal-dodecahedral duoprism has the following Coxeter diagrams:
 * x6o x5o3o (full symmetry)
 * x3x x5o3o (hexagons as ditrigons)