Dodecagonal-truncated tetrahedral duoprism

The dodecagonal-truncated tetrahedral duoprism or twatut is a convex uniform duoprism that consists of 12 truncated tetrahedral prisms, 4 hexagonal-dodecagonal duoprisms, and 4 triangular-dodecagonal duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-dodecagonal duoprism, and 2 hexagonal-dodecagonal duoprisms.

Vertex coordinates
The vertices of a dodecagonal-truncated tetrahedral duoprism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of:
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,\frac{3\sqrt2}4,\,\frac{\sqrt2}4,\,\frac{\sqrt2}4\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,\frac{3\sqrt2}4,\,\frac{\sqrt2}4,\,\frac{\sqrt2}4\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,\frac{3\sqrt2}4,\,\frac{\sqrt2}4,\,\frac{\sqrt2}4\right).$$

Representations
A dodecagonal-truncated tetrahedral duoprism has the following Coxeter diagrams:
 * x12o x3x3o (full symmetry)
 * x6x x3x3o (A3×G2 symmetry, dodecagons as dihexagons)