Hexagonal-heptagonal duoprismatic prism

The hexagonal-heptagonal duoprismatic prism or hahep, also known as the hexagonal-heptagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 hexagonal-heptagonal duoprisms, 6 square-heptagonal duoprisms and 7 square-hexagonal duoprisms. Each vertex joins 2 square-hexagonal duoprisms, 2 square-heptagonal duoprisms, and 1 hexagonal-heptagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates
The vertices of a hexagonal-heptagonal duoprismatic prism of edge length 2sin(π/7) are given by: where j = 2, 4, 6.
 * $$\left(0,\,±2\sin\frac\pi7,\,1,\,0,\,±\sin\frac\pi7\right),$$
 * $$\left(±\sqrt3\sin\frac\pi7,\,±\sin\frac\pi7,\,1,\,0,\,±\sin\frac\pi7\right),$$
 * $$\left(0,\,±2\sin\frac\pi7,\,\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,±\sin\frac\pi7\right),$$
 * $$\left(±\sqrt3\sin\frac\pi7,\,±\sin\frac\pi7,\,\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,±\sin\frac\pi7\right),$$

Representations
A hexagonal-heptagonal duoprismatic prism has the following Coxeter diagrams:
 * x x6o x7o (full symmetry)
 * x x3x x7o (hexagons as ditrigons)
 * xx6oo xx7oo&#x (hexagonal-heptagonal duoprism atop hexagonal-heptagonal duoprism)
 * xx3xx xx7oo&#x