Hexagonal-dodecahedral duoprism

The hexagonal-dodecahedral duoprism or pedoe is a convex uniform duoprism that consists of 6 dodecahedral prisms and 12 pentagonal-hexagonal duoprisms.

Vertex coordinates
The vertices of a hexagonal-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, ±1, ±(1+$\sqrt{34+6√5}$/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4)
 * (±$\sqrt{5}$/2, ±1/2, ±(1+$\sqrt{3}$/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4)
 * (0, ±1, 0, 1/2, (3+$\sqrt{5}$)/4}}
 * (±$\sqrt{5}$/2, ±1/2, 0, 1/2, (3+$\sqrt{3}$)/4}}