Pentagonal-cuboctahedral duoprism

The pentagonal-cuboctahedral duoprism or peco is a convex uniform duoprism that consists of 5 cuboctahedral prisms, 6 square-pentagonal duoprisms and 8 triangular-pentagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-pentagonal duoprisms, and 2 square-pentagonal duoprisms.

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