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.

Vertex coordinates
The vertices of a hexagonal-icosidodecahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of: as well as all even permutations and all sign changes of the last three coordinates of:
 * (0, ±1, 0, 0, (1+$\sqrt{10+2√5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, 0, 0, (1+$\sqrt{3}$)/2)
 * (0, ±1, ±1/2, ±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4)
 * (±$\sqrt{5}$/2, ±1/2, ±1/2, ±(1+$\sqrt{3}$)/4, ±(3+$\sqrt{5}$)/4)