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.

Vertex coordinates
The vertices of a pentagonal-great rhombicosidodecahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of: along with all even permutations and all sign changes of the last three coordinates of:
 * (0, $\sqrt{825+310√5}$/10, ±1/2, ±1/2, ±(3+2$\sqrt{50+10√5}$)/2)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, ±1/2, ±1/2, ±(3+2$\sqrt{50–10√5}$)/2)
 * (±1/2, –$\sqrt{5}$/10, ±1/2, ±1/2, ±(3+2$\sqrt{25+10√5}$)/2)
 * (0, $\sqrt{5}$/10, ±1/2, ±(2+$\sqrt{50+10√5}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, ±1/2, ±(2+$\sqrt{50–10√5}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±1/2, –$\sqrt{5}$/10, ±1/2, ±(2+$\sqrt{25+10√5}$)/2, ±(4+$\sqrt{5}$)/4)
 * (0, $\sqrt{5}$/10, ±1, ±(3+$\sqrt{50+10√5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, ±1, ±(3+$\sqrt{50–10√5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±1/2, –$\sqrt{5}$/10, ±1, ±(3+$\sqrt{25+10√5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (0, $\sqrt{5}$/10, ±(3+$\sqrt{50+10√5}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, ±(3+$\sqrt{50–10√5}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±1/2, –$\sqrt{5}$/10, ±(3+$\sqrt{25+10√5}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (0, $\sqrt{5}$/10, ±(1+$\sqrt{50+10√5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{5}$/20, ±(1+$\sqrt{50–10√5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±1/2, –$\sqrt{5}$/10, ±(1+$\sqrt{25+10√5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)