Octagonal-dodecahedral duoprism

The octagonal-dodecahedral duoprism or odoe is a convex uniform duoprism that consists of 8 dodecahedral prisms and 12 pentagonal-octagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal-octagonal duoprisms.

Vertex coordinates
The vertices of an octagonal-dodecahedral duoprism of edge length 1 are given by: as well as all even permutations of the last three coordinates of:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4}\right).$$

Representations
An octagonal-dodecahedral duoprism has the following Coxeter diagrams:
 * x8o x5o3o (full symmetry)
 * x4x x5o3o (octagons as ditetragons)