Pentagonal-dodecahedral duoprism

The pentagonal-dodecahedral duoprism or pedoe is a convex uniform duoprism that consists of 5 dodecahedral prisms and 12 pentagonal duoprisms.

Vertex coordinates
The vertices of a pentagonal-dodecahedral duoprism of edge length 1 are given by: as well as all even permutations and all sign changes of the last three coordinates of:
 * (0, $\sqrt{650+190√5}$/10, ±(1+$\sqrt{50+10√5}$/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, ±(1+$\sqrt{50–10√5}$/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4)
 * (±1/2, –$\sqrt{5}$/10, ±(1+$\sqrt{25+10√5}$/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4)
 * (0, $\sqrt{5}$/10, 0, 1/2, (3+$\sqrt{50+10√5}$)/4)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, 0, 1/2, (3+$\sqrt{50–10√5}$)/4)
 * (±1/2, –$\sqrt{5}$/10, 0, 1/2, (3+$\sqrt{25+10√5}$)/4)