Decagonal-truncated dodecahedral duoprism

The decagonal-truncated dodecahedral duoprism or datid is a convex uniform duoprism that consists of 10 truncated dodecahedral prisms, 12 decagonal duoprisms and 20 triangular-decagonal duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-decagonal duoprism, and 2 decagonal duoprisms.

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

Representations
A decagonal-truncated dodecahedral duoprism has the following Coxeter diagrams:
 * x10o x5x3o (full symmetry)
 * x5x x5x3o (decagons as dipentagons)