Hexagonal-octagonal duoprismatic prism

The hexagonal-octagonal duoprismatic prism or haop, also known as the hexagonal-octagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 hexagonal-octagonal duoprisms, 6 square-octagonal duoprisms, and 8 square-hexagonal duoprisms. Each vertex joins 2 square-hexagonal duoprisms, 2 square-octagonal duoprisms, and 1 hexagonal-octagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

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

Vertex coordinates
The vertices of a hexagonal-octagonal duoprismatic prism of edge length 1 are given by all permutations of the third and fourth coordinates of:
 * $$\left(0,\,±1,\,±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12\right).$$

Representations
A hexagonal-octagonal duoprismatic prism has the following Coxeter diagrams:
 * x x6o x8o (full symmetry)
 * x x3x x8o (hexagons as ditrigons)
 * x x6o x4x (octagons as ditetragons)
 * x x3x x4x
 * xx6oo xx8oo&#x (hexagonal-octagonal duoprism atop hexagonal-octagonal duoprism)
 * xx3xx xx8oo&#x
 * xx6oo xx4xx&#x
 * xx3xx xx4xx&#x