Heptagonal-pentagonal antiprismatic duoprism

The heptagonal-pentagonal antiprismatic duoprism or hepap is a convex uniform duoprism that consists of 7 pentagonal antiprismatic prisms, 2 pentagonal-heptagonal duoprisms, and 10 triangular-heptagonal duoprisms. Each vertex joins 2 pentagonal antiprismatic prisms, 3 triangular-heptagonal duoprisms, and 1 pentagonal-heptagonal duoprism.

Vertex coordinates
The vertices of a heptagonal-pentagonal antiprismatic duoprism of edge length 2sin(π/7) are given by all central inversions of the last three coordinates of: where j = 2, 4, 6.
 * $$\left(1,\,0,\,0,\,2\sqrt{\frac{5+\sqrt5}{10}}\sin\frac\pi7,\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac\pi7\right),$$
 * $$\left(\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,0,\,2\sqrt{\frac{5+\sqrt5}{10}}\sin\frac\pi7,\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac\pi7\right),$$
 * $$\left(1,\,0,\,±\frac{(1+\sqrt5)\sin\frac\pi7}2,\,\sqrt{\frac{5-\sqrt5}{10}}\sin\frac\pi7,\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac\pi7\right),$$
 * $$\left(\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,±\frac{(1+\sqrt5)\sin\frac\pi7}2,\,\sqrt{\frac{5-\sqrt5}{10}}\sin\frac\pi7,\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac\pi7\right),$$
 * $$\left(1,\,0,\,±\sin\frac\pi7,\,-\sqrt{\frac{5-2\sqrt5}{5}}\sin\frac\pi7,\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac\pi7\right),$$
 * $$\left(\cos\frac{j\pi}7,\,±\sin\frac{j\pi}7,\,±\sin\frac\pi7,\,-\sqrt{\frac{5-2\sqrt5}{5}}\sin\frac\pi7,\,\sqrt{\frac{5+\sqrt5}{10}}\sin\frac\pi7\right),$$

Representations
A heptagonal-pentagonal antiprismatic duoprism has the following Coxeter diagrams:
 * x7o s2s10o (full symmetry; pentagonal antiprisms as alternated decagonal prisms)
 * x7o s2s5s (pentagonal antiprisms as alternated dipentagonal prisms)