Hexagonal-truncated dodecahedral duoprism

The hexagonal-truncated dodecahedral duoprism or hatid is a convex uniform duoprism that consists of 6 truncated dodecahedral prisms, 12 hexagonal-decagonal duoprisms and 20 triangular-hexagonal duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-hexagonal duoprism, and 2 hexagonal-decagonal duoprisms.

Vertex coordinates
The vertices of a hexagonal-truncated dodecahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:
 * $$\left(0,\,±1,\,0,\,±\frac12,\,±\frac{5+3\sqrt5}4\right),$$
 * $$\left(0,\,±1,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(0,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,0,\,±\frac12,\,±\frac{5+3\sqrt5}4\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{2+\sqrt5}2\right).$$

Representations
A hexagonal-truncated dodecahedral duoprism has the following Coxeter diagrams:
 * x6o x5x3o (full symmetry)
 * x3x x5x3o (hexagons as ditrigons)