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.

Vertex coordinates
The vertices of a hexagonal-truncated icosahedral 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, (3+3$\sqrt{74+18√5}$)/4)
 * (0, ±1, 1/2, (5+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * (0, ±1, (1+$\sqrt{5}$)/4, 1, (2+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, 0, 1/2, (3+3$\sqrt{3}$)/4)
 * (±$\sqrt{5}$/2, ±1/2, 1/2, (5+$\sqrt{3}$)/4, (1+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, (1+$\sqrt{3}$)/4, 1, (2+$\sqrt{5}$)/2)