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. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-hexagonal duoprism, and 2 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:
 * $$\left(±1,\,0,\,\frac{3\sqrt2}4,\,\frac{\sqrt2}4,\,\frac{\sqrt2}4\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}2,\,\frac{3\sqrt2}4,\,\frac{\sqrt2}4,\,\frac{\sqrt2}4\right).$$

Representations
A hexagonal-truncated tetrahedral duoprism has the following Coxeter diagrams:
 * x6o x3x3o (full symmetry)
 * x3x x3x3o (hexagons as ditrigons)