Hexagonal-truncated octahedral duoprism

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

This polyteron can be alternated into a triangular-pyritohedral icosahedral duoantiprism, although it cannot be made uniform.

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

Representations
A hexagonal-truncated octahedral duoprism has the following Coxeter diagrams:
 * x6o o4x3x (full symmetry)
 * x6o x3x3x
 * x3x o4x3x (hexagons as ditrigons)
 * x3x x3x3x