Decagonal-great rhombicosidodecahedral duoprism

The decagonal-great rhombicosidodecahedral duoprism or dagrid is a convex uniform duoprism that consists of 10 great rhombicosidodecahedral prisms, 12 decagonal duoprisms, 20 hexagonal-decagonal duoprisms and 30 square-decagonal duoprisms.

This polyteron can be alternated into a pentagonal-snub dodecahedral duoantiprism, although it cannot be made uniform.

Vertex coordinates
The vertices of a decagonal-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, ±(1+$\sqrt{37+14√5}$)/2, ±1/2, ±1/2, ±(3+2$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4, ±1/2, ±1/2, ±(3+2$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, ±1/2, ±1/2, ±(3+2$\sqrt{5+2√5}$)/2)
 * (0, ±(1+$\sqrt{5}$)/2, ±1/2, ±(2+$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4, ±1/2, ±(2+$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±$\sqrt{5}$/2, ±1/2, ±1/2, ±(2+$\sqrt{5+2√5}$)/2, ±(4+$\sqrt{5}$)/4)
 * (0, ±(1+$\sqrt{5}$)/2, ±1, ±(3+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4, ±1, ±(3+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±$\sqrt{5}$/2, ±1/2, ±1, ±(3+$\sqrt{5+2√5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (0, ±(1+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4, ±(3+$\sqrt{5}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, ±(3+$\sqrt{5+2√5}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (0, ±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4, ±(1+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±$\sqrt{5}$/2, ±1/2, ±(1+$\sqrt{5+2√5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)