Dodecagonal-truncated dodecahedral duoprism

The dodecagonal-truncated dodecahedral duoprism or twatid is a convex uniform duoprism that consists of 12 truncated dodecahedral prisms, 12 decagonal-dodecagonal duoprisms and 20 triangular-dodecagonal duoprisms.

Vertex coordinates
The vertices of a dodecagonal-truncated dodecahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (±(1+$\sqrt{106+2√1317+240√15}$)/2, ±(1+$\sqrt{3}$)/2, 0, 1/2, (5+3$\sqrt{3}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{3}$)/2, 1/2, (3+$\sqrt{3}$)/4, (3+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{3}$)/2, (3+$\sqrt{3}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)
 * (±1/2, ±(2+$\sqrt{5}$)/2, 0, 1/2, (5+3$\sqrt{3}$)/4)
 * (±1/2, ±(2+$\sqrt{5}$)/2 1/2, (3+$\sqrt{3}$)/4, (3+$\sqrt{5}$)/2)
 * (±1/2, ±(2+$\sqrt{5}$)/2, (3+$\sqrt{3}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±1/2, 0, 1/2, (5+3$\sqrt{3}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±1/2, 1/2, (3+$\sqrt{3}$)/4, (3+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±1/2, (3+$\sqrt{3}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)