Pentagonal-small rhombicosidodecahedral duoprism

The pentagonal-small rhombicosidodecahedral duoprism or pesrid is a convex uniform duoprism that consists of 5 small rhombicosidodecahedral prisms, 12 pentagonal duoprisms, 30 square-pentagonal duoprisms, and 20 triangular-pentagonal duoprisms. Each vertex joins 2 small rhombicosidodecahedral prisms, 1 triangular-pentagonal duoprism, 2 square-pentagonal duoprisms, and 1 pentagonal duoprism.

Vertex coordinates
The vertices of a pentagonal-small rhombicosidodecahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of: as well as all even permutations of the last three coordinates of:
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\, \sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,0,\,±\frac{3+\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\, \sqrt{\frac{5-\sqrt5}{40}},\,0,\,±\frac{3+\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,±\frac{3+\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,±\frac{1+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{3+\sqrt5}4\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\, \sqrt{\frac{5-\sqrt5}{40}},\,±\frac{1+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{3+\sqrt5}4\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{1+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{3+\sqrt5}4\right).$$