Pentagonal-great rhombicuboctahedral duoprism

The pentagonal-great rhombicuboctahedral duoprism or pegirco is a convex uniform duoprism that consists of 5 great rhombicuboctahedral prisms, 6 pentagonal-octagonal duoprisms, 8 pentagonal-hexagonal duoprisms, and 8 square-pentagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-pentagonal duoprism, 1 pentagonal-hexagonal duoprism, and 1 pentagonal-octagonal duoprism.

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