Dodecagonal-great rhombicosidodecahedral duoprism

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

This polychoron can be alternated into a hexagonal-snub dodecahedral duoantiprism, although it cannot be made uniform. The dodecagons can also be alternated into long ditrigons to create a bialternatosnub snub dodecahedral-hexagonal duoprism, which is also nonuniform.

Vertex coordinates
The vertices of a dodecagonal-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:
 * (±(1+$\sqrt{31+12√5+csc^{2}π/11}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2, ±1/2, ±(3+2$\sqrt{3}$)/2)
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±1/2, ±1/2, ±(3+2$\sqrt{3}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±1/2, ±1/2, ±1/2, ±(3+2$\sqrt{3}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±1/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{3}$)/2, ±1, ±(3+$\sqrt{3}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±1, ±(3+$\sqrt{3}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±1/2, ±1, ±(3+$\sqrt{3}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{3}$)/2, ±(3+$\sqrt{3}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±(3+$\sqrt{3}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±1/2, ±(3+$\sqrt{3}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±(1+$\sqrt{3}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±1/2, ±(1+$\sqrt{3}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)