Heptagonal-decagonal duoprism

The heptagonal-decagonal duoprism or hedadip, also known as the 7-10 duoprism, is a uniform duoprism that consists of 7 decagonal prisms and 10 heptagonal prisms, with two of each joining at each vertex.

Vertex coordinates
The coordinates of a heptagonal-decagonal duoprism, centered at the origin and with edge length 2sin(π/7), are given by: where j = 2, 4, 6.
 * $$\left(1,0,±\sin\frac\pi7,±\sqrt{5+2\sqrt5}\sin\frac\pi7\right),$$
 * $$\left(1,0,±\frac{3+\sqrt5}2\sin\frac\pi7,±\sqrt{\frac{5+\sqrt5}2}\sin\frac\pi7\right),$$
 * $$\left(1,0,\left(1+\sqrt5\right)\sin\frac\pi7,0\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),±\sin\left(\frac{j\pi}7\right),±\sin\frac\pi7,±\sqrt{5+2\sqrt5}\sin\frac\pi7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),±\sin\left(\frac{j\pi}7\right),±\frac{3+\sqrt5}2\sin\frac\pi7,±\sqrt{\frac{5+\sqrt5}2}\sin\frac\pi7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),±\sin\left(\frac{j\pi}7\right),\left(1+\sqrt5\right)\sin\frac\pi7,0\right),$$

Representations
A heptagonal-decagonal duoprism has the following Coxeter diagrams:
 * x7o x10o (full symmetry)
 * x5x x7o (decagons as dipentagons)