Pentagonal-truncated icosahedral duoprism

The pentagonal-truncated icosahedral duoprism or peti is a convex uniform duoprism that consists of 5 truncated icosahedral prisms, 20 pentagonal-hexagonal duoprisms and 12 pentagonal duoprisms.

Vertex coordinates
The vertices of a pentagonal-truncated icosahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (0, $\sqrt{1650+490√5}$/10, 0, 1/2, (3+3$\sqrt{50+10√5}$)/4)
 * (0, $\sqrt{5}$/10, 1/2, (5+$\sqrt{50+10√5}$)/4, (1+$\sqrt{5}$)/2)
 * (0, $\sqrt{5}$/10, (1+$\sqrt{50+10√5}$)/4, 1, (2+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, 0, 1/2, (3+3$\sqrt{50–10√5}$)/4)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, 1/2, (5+$\sqrt{50–10√5}$)/4, (1+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, (1+$\sqrt{50–10√5}$)/4, 1, (2+$\sqrt{5}$)/2)
 * (±1/2, –$\sqrt{5}$/10, 0, 1/2, (3+3$\sqrt{25+10√5}$)/4)
 * (±1/2, –$\sqrt{5}$/10, 1/2, (5+$\sqrt{25+10√5}$)/4, (1+$\sqrt{5}$)/2)
 * (±1/2, –$\sqrt{5}$/10, (1+$\sqrt{25+10√5}$)/4, 1, (2+$\sqrt{5}$)/2)