Dodecagonal-truncated dodecahedral duoprism

The dodecagonal-truncated dodecahedral duoprism or twatid is a convex uniform duoprism that consists of 12 truncated dodecahedral prisms, 12 decagonal-dodecagonal duoprisms and 20 triangular-dodecagonal duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-dodecagonal duoprism, and 2 decagonal-dodecagonal duoprisms.

Vertex coordinates
The vertices of a dodecagonal-truncated dodecahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,0,\,±\frac12,\,±\frac{5+3\sqrt5}4\right),$$
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,0,\,±\frac12,\,±\frac{5+3\sqrt5}4\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,0,\,±\frac12,\,±\frac{5+3\sqrt5}4\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{2+\sqrt5}2\right).$$

Representations
A dodecagonal-truncated dodecahedral duoprism has the following Coxeter diagrams:
 * x12o x5x3o (full symmetry)
 * x6x x5x3o (dodecagons as dihexagons)