Hexagonal-truncated icosahedral duoprism

The hexagonal-truncated icosahedral duoprism or hati is a convex uniform duoprism that consists of 6 truncated icosahedral prisms, 20 hexagonal duoprisms and 12 pentagonal-hexagonal duoprisms. Each vertex joins 2 truncated icosahedral prisms, 1 pentagonal-hexagonal duoprism, and 2 hexagonal duoprisms.

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

Representations
A hexagonal-truncated icosahedral duoprism has the following Coxeter diagrams:
 * x6o o5x3x (full symmetry)
 * x3x o5x3x (hexagons as ditrigons)