Pentagonal-truncated octahedral duoprism

The pentagonal-truncated octahedral duoprism or petoe is a convex uniform duoprism that consists of 5 truncated octahedral prisms, 8 pentagonal-hexagonal duoprisms and 6 square-pentagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-pentagonal duoprism, and 2 pentagonal-hexagonal duoprisms.

Vertex coordinates
The vertices of a pentagonal-truncated octahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,0,\,±\frac{\sqrt2}2,\,±\sqrt2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,0,\,±\frac{\sqrt2}2,\,±\sqrt2\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,±\frac{\sqrt2}2,\,±\sqrt2\right).$$