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.

Vertex coordinates
The vertices of a hexagonal-truncated dodecahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (0, ±1, 0, 1/2, (5+3$\sqrt{90+30√5}$)/4)
 * (0, ±1, 1/2, (3+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2)
 * (0, ±1, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, 0, 1/2, (5+3$\sqrt{3}$)/4)
 * (±$\sqrt{5}$/2, ±1/2, 1/2, (3+$\sqrt{3}$)/4, (3+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, (3+$\sqrt{3}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)