Decagonal-truncated icosahedral duoprism

The decagonal-truncated icosahedral duoprism or dati is a convex uniform duoprism that consists of 10 truncated icosahedral prisms, 20 hexagonal-decagonal duoprisms and 12 pentagonal-decagonal duoprisms.

Vertex coordinates
The vertices of a decagonal-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+$\sqrt{82+26√5}$)/2, 0, 1/2, (3+3$\sqrt{5}$)/4)
 * (0, ±(1+$\sqrt{5}$)/2, 1/2, (5+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * (0, ±(1+$\sqrt{5}$)/2, (1+$\sqrt{5}$)/4, 1, (2+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4, 0, 1/2, (3+3$\sqrt{5}$)/4)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4, 1/2, (5+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4, (1+$\sqrt{5}$)/4, 1, (2+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, 0, 1/2, (3+3$\sqrt{5+2√5}$)/4)
 * (±$\sqrt{5}$/2, ±1/2, 1/2, (5+$\sqrt{5+2√5}$)/4, (1+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, (1+$\sqrt{5+2√5}$)/4, 1, (2+$\sqrt{5}$)/2)