Dodecagonal-cuboctahedral duoprism

The dodecagonal-cuboctahedral duoprism or twaco is a convex uniform duoprism that consists of 12 cuboctahedral prisms, 6 square-dodecagonal duoprisms and 8 triangular-dodecagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-dodecagonal duoprisms, and 2 square-dodecagonal duoprisms.

Vertex coordinates
The vertices of a dodecagonal-cuboctahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,0,\,±\frac{\sqrt2}2,\,±\frac{\sqrt2}2\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,0,\,±\frac{\sqrt2}2,\,±\frac{\sqrt2}2\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,0,\,±\frac{\sqrt2}2,\,±\frac{\sqrt2}2\right).$$

Representations
A dodecagonal-cuboctahedral duoprism has the following Coxeter diagrams:
 * x12o o4x3o (full symmetry)
 * x6x o4x3o (dodecagons as dihexagons)
 * x12o x3o3x
 * x6x x3o3x