Hexagonal-octahedral duoprism

The hexagonal-octahedral duoprism or hoct is a convex uniform duoprism that consists of 6 octahedral prisms and 8 triangular-hexagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-hexagonal duoprisms.

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

Representations
A hexagonal-octahedral duoprism has the following Coxeter diagrams:
 * x6o o4o3x (full symmetry)
 * x3x o4o3x (hexagons as ditrigons)
 * x6o o3x3o (octahedra as tetratetrahedra)
 * x3x o3x3o (hexagons as ditrigons and octahedra as tetratetrahedra)
 * xo3ox xx6oo&#x (triangular-hexagonal duoprism atop triangle-gyrated triangular-hexagonal duoprism)
 * xo3ox xx3xx&#x