Pentagonal-truncated dodecahedral duoprism

The pentagonal-truncated dodecahedral duoprism or petid is a convex uniform duoprism that consists of 5 truncated dodecahedral prisms, 12 pentagonal-decagonal duoprisms and 20 triangular-pentagonal duoprisms.

Vertex coordinates
The vertices of a pentagonal-truncated dodecahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (0, $\sqrt{2050+790√5}$/10, 0, 1/2, (5+3$\sqrt{50+10√5}$)/4)
 * (0, $\sqrt{5}$/10, 1/2, (3+$\sqrt{50+10√5}$)/4, (3+$\sqrt{5}$)/2)
 * (0, $\sqrt{5}$/10, (3+$\sqrt{50+10√5}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, 0, 1/2, (5+3$\sqrt{50–10√5}$)/4)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, 1/2, (3+$\sqrt{50–10√5}$)/4, (3+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, (3+$\sqrt{50–10√5}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)
 * (±1/2, –$\sqrt{5}$/10, 0, 1/2, (5+3$\sqrt{25+10√5}$)/4)
 * (±1/2, –$\sqrt{5}$/10, 1/2, (3+$\sqrt{25+10√5}$)/4, (3+$\sqrt{5}$)/2)
 * (±1/2, –$\sqrt{5}$/10, (3+$\sqrt{25+10√5}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)