Pentagonal-dodecahedral duoprism

The pentagonal-dodecahedral duoprism or pedoe is a convex uniform duoprism that consists of 5 dodecahedral prisms and 12 pentagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal duoprisms.

Vertex coordinates
The vertices of a pentagonal-dodecahedral duoprism of edge length 1 are given by: as well as all even permutations of the last three coordinates of:
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\, \sqrt{\frac{5-\sqrt5}{40}},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\, \sqrt{\frac{5-\sqrt5}{40}},\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4}\right).$$