Pentagonal-small rhombicuboctahedral duoprism

The pentagonal-small rhombicuboctahedral duoprism or pesirco is a convex uniform duoprism that consists of 5 small rhombicuboctahedral prisms, 18 square-pentagonal duoprisms of two kinds and 8 triangular-pentagonal duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangular-pentagonal duoprism, and 3 square-pentagonal duoprisms.

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