Decagonal-truncated tetrahedral duoprism

The decagonal-truncated tetrahedral duoprism or datut is a convex uniform duoprism that consists of 10 truncated tetrahedral prisms, 4 hexagonal-decagonal duoprisms and 4 triangular-decagonal duoprisms.

Vertex coordinates
The vertices of a decagonal-truncated tetrahedral duoprism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of:
 * (0, ±(1+$\sqrt{46+8√5}$)/2, $\sqrt{5}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)
 * (±$\sqrt{2}$/4, ±(3+$\sqrt{10+2√5}$)/4, $\sqrt{5}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)
 * (±$\sqrt{2}$/2, ±1/2, $\sqrt{5+2√5}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)