Dodecagonal-icosidodecahedral duoprism

The dodecagonal-icosidodecahedral duoprism or twid is a convex uniform duoprism that consists of 12 icosidodecahedral prisms, 12 pentagonal-dodecagonal duoprisms, and 20 triangular-dodecagonal duoprisms. Each vertex joins 2 icosidodecahedral prisms, 2 triangular-dodecagonal duoprisms, and 2 pentagonal-dodecagonal duoprisms.

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

Representations
A dodecagonal-icosidodecahedral duoprism has the following Coxeter diagrams:
 * x12o o5x3o (full symmetry)
 * x6x o5x3o (dodecagons as dihexagons)