Dodecagonal-truncated octahedral duoprism

The dodecagonal-truncated octahedral duoprism or twatoe is a convex uniform duoprism that consists of 12 truncated octahedral prisms, 8 hexagonal-dodecagonal duoprisms and 6 square-dodecagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-dodecagonal duoprism, and 2 hexagonal-dodecagonal duoprisms.

This polyteron can be alternated into a hexagonal-pyritohedral icosahedral duoantiprism, although it cannot be made uniform. The dodecagons can also be alternated into long ditrigons to create a pyritohedral icosahedral-hexagonal prismantiprismoid, which is also nonuniform.

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

Representations
A dodecagonal-truncated octahedral duoprism has the following Coxeter diagrams:
 * x12o o4x3x (full symmetry)
 * x12o x3x3x
 * x6x o4x3x (dodecagons as dihexagons)
 * x6x x3x3x