Dodecagonal-truncated tetrahedral duoprism

The dodecagonal-truncated tetrahedral duoprism or twatut is a convex uniform duoprism that consists of 12 truncated tetrahedral prisms, 4 hexagonal-dodecagonal duoprisms and 4 triangular-dodecagonal duoprisms.

Vertex coordinates
The vertices of a dodecagonal-truncated tetrahedral duoprism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of:
 * (±(1+$\sqrt{54+16√3}$)/2, ±(1+$\sqrt{3}$)/2, $\sqrt{3}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)
 * (±1/2, ±(2+$\sqrt{2}$)/2, $\sqrt{3}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)
 * (±(2+$\sqrt{2}$)/2, ±1/2, $\sqrt{3}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)