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.

Vertex coordinates
The vertices of a pentagonal-cuboctahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of:
 * (0, $\sqrt{150+10√5}$/10, 0, $\sqrt{50+10√5}$/2, $\sqrt{2}$/2)
 * (±(1+$\sqrt{2}$)/4, $\sqrt{5}$/20, 0, $\sqrt{50–10√5}$/2, $\sqrt{2}$/2)
 * (±1/2, –$\sqrt{2}$/10, 0, $\sqrt{25+10√5}$/2, $\sqrt{2}$/2)