Dodecagonal-tetrahedral duoprism

The dodecagonal-tetrahedral duoprism or twatet is a convex uniform duoprism that consists of 12 tetrahedral prisms and 4 triangular-dodecagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-dodecagonal duoprisms.

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

Representations
A dodecagonal-tetrahedral duoprism has the following Coxeter diagrams:
 * x12o x3o3o (full symmetry)
 * x6x x3o3o (dodecagons as dihexagons)