Pentagonal-great rhombicosidodecahedral duoprism

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

Vertex coordinates
The vertices of a pentagonal-great rhombicosidodecahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of: along with all even permutations of the last three coordinates of:
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right).$$