Dodecagonal-dodecahedral duoprism

The dodecagon-dodecahedral duoprism or twadoe is a convex uniform duoprism that consists of 12 dodecahedral prisms and 12 pentagonal-dodecagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal-dodecagonal duoprisms.

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

Representations
A dodecagonal-dodecahedral duoprism has the following Coxeter diagrams:
 * x12o x5o3o (full symmetry)
 * x6x x5o3o (dodecagons as dihexagons)