Dodecagonal-octahedral duoprism

The dodecagonal-octahedral duoprism or twoct is a convex uniform duoprism that consists of 12 octahedral prisms and 8 triangular-dodecagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-dodecagonal duoprisms.

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

Representations
A dodecahedral-octahedral duoprism has the following Coxeter diagrams:
 * x12o o4o3x (full symmetry)
 * x6x o3x3o (dodecagons as dihexagons)
 * x12o o4o3x (octahedra as tetratetrahedra)
 * x6x o3x3o (dodecagons as dihexagons and octahedra as tetratetrahedra)