Hexagonal-tetrahedral duoprism

The hexagonal-tetrahedral duoprism or hatet is a convex uniform duoprism that consists of 6 tetrahedral prisms and 4 triangular-hexagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-hexagonal duoprisms.

Vertex coordinates
The vertices of a hexagonal-tetrahedral duoprism of edge length 1 are given by all even sign changes of the last three coordinates of:
 * $$\left(±1,\,0,\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

Representations
A hexagonal-tetrahedral duoprism has the following Coxeter diagrams:
 * x6o x3o3o (full symmetry)
 * x3x x3o3o (hexagons as ditrigons)
 * ox3oo xx6oo&#x (hexagon atop triangular-hexagonal duoprism)
 * ox3oo xx3xx&#x
 * ox xo xx6oo&#x (hexagonal prism atop orthogonal hexagonal prism)
 * ox xo xx3xx&#x
 * oox xxx3xxx&#x
 * xxxx3xxxx&#x