Pentagonal-truncated icosahedral duoprism

The pentagonal-truncated icosahedral duoprism or peti is a convex uniform duoprism that consists of 5 truncated icosahedral prisms, 20 pentagonal-hexagonal duoprisms and 12 pentagonal duoprisms. Each vertex joins 2 truncated icosahedral prisms, 1 pentagonal duoprism, and 2 pentagonal-hexagonal duoprisms.

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