Triangular-great rhombicosidodecahedral duoprism

The triangular-great rhombicosidodecahedral duoprism or tragrid is a convex uniform duoprism that consists of 3 great rhombicosidodecahedral prisms, 12 triangular-decagonal duoprisms, 20 triangular-hexagonal duoprisms and 30 triangular-square duoprisms.

Vertex coordinates
The vertices of a triangular-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, $\sqrt{291+108√5}$/3, ±1/2, ±1/2, ±(3+2$\sqrt{3}$)/2)
 * (±1/2, -$\sqrt{5}$/6, ±1/2, ±1/2, ±(3+2$\sqrt{3}$)/2)
 * (0, $\sqrt{5}$/3, ±1/2, ±(2+$\sqrt{3}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±1/2, -$\sqrt{5}$/6, ±1/2, ±(2+$\sqrt{3}$)/2, ±(4+$\sqrt{5}$)/4)
 * (0, $\sqrt{5}$/3, ±1, ±(3+$\sqrt{3}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±1/2, -$\sqrt{5}$/6, ±1, ±(3+$\sqrt{3}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (0, $\sqrt{5}$/3, ±(3+$\sqrt{3}$)/4, ±3(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±1/2, -$\sqrt{5}$/6, ±(3+$\sqrt{3}$)/4, ±3(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (0, $\sqrt{5}$/3, ±(1+$\sqrt{3}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±1/2, -$\sqrt{5}$/6, ±(1+$\sqrt{3}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)