Pentagonal-icosidodecahedral duoprism

The pentagonal-icosidodecahedral duoprism or pid is a convex uniform duoprism that consists of 5 icosidodecahedral prisms, 12 pentagonal duoprisms and 20 triangular-pentagonal duoprisms.

Vertex coordinates
The vertices of a pentagonal-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, $\sqrt{50+15√5}$/10, 0, 0, (1+$\sqrt{50+10√5}$)/2)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, 0, 0, (1+$\sqrt{50–10√5}$)/2)
 * (±1/2, –$\sqrt{5}$/10, 0, 0, (1+$\sqrt{25+10√5}$)/2)
 * (0, $\sqrt{5}$/10, ±1/2, ±(1+$\sqrt{50+10√5}$)/4, ±(3+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, ±1/2, ±(1+$\sqrt{50–10√5}$)/4, ±(3+$\sqrt{5}$)/4)
 * (±1/2, –$\sqrt{5}$/10, ±1/2, ±(1+$\sqrt{25+10√5}$)/4, ±(3+$\sqrt{5}$)/4)