Hexagonal-icosidodecahedral duoprism

The hexagonal-icosidodecahedral duoprism or hid is a convex uniform duoprism that consists of 6 icosidodecahedral prisms, 12 pentagonal-hexagonal duoprisms, and 20 triangular-hexagonal duoprisms. Each vertex joins 2 icosidodecahedral prisms, 2 triangular-hexagonal duoprisms, and 2 pentagonal-hexagonal duoprisms.

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

Representations
A hexagonal-icosidodecahedral duoprism has the following Coxeter diagrams:
 * x6o o5x3o (full symmetry)
 * x3x o5x3o (hexagons as ditrigons)