Heptagonal-square antiprismatic duoprism

The heptagonal-square antiprismatic duoprism or hesquap is a convex uniform duoprism that consists of 7 square antiprismatic prisms, 2 square-heptagonal duoprisms and 8 triangular-heptagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-heptagonal duoprisms, and 1 square-heptagonal duoprism.

Vertex coordinates
The vertices of a heptagonal-square antiprismatic duoprism of edge length 2sin(π/7) are given by: where j = 2, 4, 6.
 * $$\left(1,\,0,\,±\sin\frac\pi7,\,±\sin\frac\pi7,\,\frac{\sqrt[4]8\sin\frac\pi7}2\right),$$
 * $$\left(\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,±\sin\frac\pi7,\,±\sin\frac\pi7,\,\frac{\sqrt[4]8\sin\frac\pi7}2\right),$$
 * $$\left(1,\,0,\,0,\,±\sqrt2\sin\frac\pi7,\,-\frac{\sqrt[4]8\sin\frac\pi7}2\right),$$
 * $$\left(\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,0,\,±\sqrt2\sin\frac\pi7,\,-\frac{\sqrt[4]8\sin\frac\pi7}2\right),$$
 * $$\left(1,\,0,\,±\sqrt2\sin\frac\pi7,\,0,\,-\frac{\sqrt[4]8\sin\frac\pi7}2\right),$$
 * $$\left(\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,±\sqrt2\sin\frac\pi7,\,0,\,-\frac{\sqrt[4]8\sin\frac\pi7}2\right),$$

Representations
A heptagonal-square antiprismatic duoprism has the following Coxeter diagrams:
 * x7o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
 * x7o s2s4s (square antiprisms as alternated ditetragonal prisms)