Hexagonal-octagonal duoprism

The hexagonal-octagonal duoprism or hodip, also known as the 6-8 duoprism, is a uniform duoprism that consists of 6 octagonal prisms and 8 hexagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a triangular-square duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a triangular-square prismantiprismoid, which is also nonuniform.

Vertex coordinates
The vertices of a hexagonal-octagonal duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,±1,\,±\frac12,\,±\frac{1+\sqrt2}{2}\right),$$
 * $$\left(0,\,±1,\,±\frac{1+\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac12,\,±\frac{1+\sqrt2}{2}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$

Representations
A hexagonal-octagonal duoprism has the following Coxeter diagrams:


 * x6o x8o (full symmetry)
 * x3x x8o (hexagons as ditetragons)
 * x4x x6o (octagons as ditetragons)
 * x3x x4x *both of above applied)*xux xxx8ooo&#xt (octagonal axial)
 * xux xxx4xxx&#xt (ditetragonal axial)
 * xwwx xxxx3xxxx&#xt (ditrigonal axial)