Hexagonal-cuboctahedral duoprism

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

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

Representations
A hexagonal-cuboctahedral duoprism has the following Coxeter diagrams:
 * x6o o4x3o (full symmetry)
 * x3x o4x3o (hexagons as ditrigons)
 * x6o x3o3x
 * x3x x3o3x
 * oxx3xxo xxx3xxx&#xt (triangular-hexagonal duoprism || pseudo hexagonal duoprism || gyro triangular-hexagonal duoprism)