Dodecagonal-truncated icosahedral duoprism

The dodecagonal-truncated icosahedral duoprism or twati is a convex uniform duoprism that consists of 12 truncated icosahedral prisms, 20 hexagonal-dodecagonal duoprisms and 12 pentagonal-dodecagonal duoprisms.

Vertex coordinates
The vertices of a dodecagonal-truncated icosahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (±(1+$\sqrt{58+18√5+4csc^{2}π/11}$)/2, ±(1+$\sqrt{3}$)/2 0, 1/2, (3+3$\sqrt{3}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{3}$)/2, 1/2, (5+$\sqrt{3}$)/4, (1+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{3}$)/2, (1+$\sqrt{3}$)/4, 1, (2+$\sqrt{5}$)/2)
 * (±1/2, ±(2+$\sqrt{5}$)/2, 0, 1/2, (3+3$\sqrt{3}$)/4)
 * (±1/2, ±(2+$\sqrt{5}$)/2, 1/2, (5+$\sqrt{3}$)/4, (1+$\sqrt{5}$)/2)
 * (±1/2, ±(2+$\sqrt{5}$)/2, (1+$\sqrt{3}$)/4, 1, (2+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±1/2, 0, 1/2, (3+3$\sqrt{3}$)/4)
 * (±(2+$\sqrt{5}$)/2, ±1/2, 1/2, (5+$\sqrt{3}$)/4, (1+$\sqrt{5}$)/2)
 * (±(2+$\sqrt{5}$)/2, ±1/2, (1+$\sqrt{3}$)/4, 1, (2+$\sqrt{5}$)/2)