Octagonal-truncated dodecahedral duoprism

The octagonal-truncated dodecahedral duoprism or otid is a convex uniform duoprism that consists of 8 truncated dodecahedral prisms, 12 octagonal-decagonal duoprisms and 20 triangular-octagonal duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-octagonal duoprism, and 2 octagonal-decagonal duoprisms.

Vertex coordinates
The vertices of an octagonal-truncated dodecahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,0,\,±\frac12,\,±\frac{5+3\sqrt5}4\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,0,\,±\frac12,\,±\frac{5+3\sqrt5}4\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{2+\sqrt5}2\right).$$

Representations
An octagonal-truncated dodecahedral duoprism has the following Coxeter diagrams:
 * x8o x5x3o (full symmetry)
 * x4x x5x3o (octagons as ditetragons)