Pentagonal-truncated cubic duoprism

The pentagonal-truncated cubic duoprism or petic is a convex uniform duoprism that consists of 5 truncated cubic prisms, 6 pentagonal-octagonal duoprisms and 8 triangular-pentagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular-pentagonal duoprism, and 2 pentagonal-octagonal duoprisms.

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