Heptagonal-octagonal duoprismatic prism

The heptagonal-octagonal duoprismatic prism or heop, also known as the heptagonal-octagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 heptagonal-octagonal duoprisms, 7 square-octagonal duoprisms, and 8 square-heptagonal duoprisms. Each vertex joins 2 square-heptagonal duoprisms, 2 square-octagonal duoprisms, and 1 heptagonal-octagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates
The vertices of a heptagonal-octagonal duoprismatic prism of edge length 2sin(π/7) are given by all permutations of the third and fourth coordinates of: where j = 2, 4, 6.
 * $$\left(1,\,0,\,±\sin\frac\pi7,\,±(1+\sqrt2)\sin\frac\pi7,\,±\sin\frac\pi7\right),$$
 * $$\left(\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,±\sin\frac\pi7,\,±(1+\sqrt2)\sin\frac\pi7,\,±\sin\frac\pi7\right),$$

Representations
A heptagonal-octagonal duoprismatic prism has the following Coxeter diagrams:
 * x x7o x8o (full symmetry)
 * x x7o x4x (octagons as ditetragons)
 * xx7oo xx8oo&#x (heptagonal-octagonal duoprism atop heptagonal-octagonal duoprism)
 * xx7oo xx4xx&#x