Hexagonal-great rhombicosidodecahedral duoprism

The hexagonal-great rhombicosidodecahedral duoprism or hagrid is a convex uniform duoprism that consists of 6 great rhombicosidodecahedral prisms, 12 hexagonal-decagonal duoprisms, 20 hexagonal duoprisms, and 30 square-hexagonal duoprisms. Each vertex joins 2 great rhombicosidodecahedral prisms, 1 square-hexagonal duoprism, 1 hexagonal duoprism, and 1 hexagonal-decagonal duoprism.

This polyteron can be alternated into a triangular-snub dodecahedral duoantiprism, although it cannot be made uniform.

Vertex coordinates
The vertices of a hexagonal-great rhombicosidodecahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of: along with all even permutations of the last three coordinates of:
 * $$\left(0,\,±1,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(0,\,±1,\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(0,\,±1,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(0,\,±1,\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(0,\,±1,\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right).$$

Representations
A hexagonal-great rhombicosidodecahedral duoprism has the following Coxeter diagrams:
 * x6o x5x3x (full symmetry)
 * x3x x5x3x (hexagons as ditrigons)