Hexagonal-truncated tetrahedral duoprism

The hexagonal-truncated tetrahedral duoprism or hatut is a convex uniform duoprism that consists of 6 truncated tetrahedral prisms, 4 hexagonal duoprisms and 4 triangular-hexagonal duoprisms.

Vertex coordinates
The vertices of a hexagonal-truncated tetrahedral duoprism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of:
 * (0, ±1, $\sqrt{38}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)
 * (±$\sqrt{2}$/2, ±1/2, $\sqrt{3}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)