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:
 * (1, 0, ±sin(π/7), ±sin(π/7)$\sqrt{(5+√5)/2}$),
 * (1, 0, ±sin(π/7)(3+$\sqrt{2}$)/2, ±sin(π/7)$\sqrt{5+2√5}$),
 * (1, 0, ±sin(π/7)(1+$\sqrt{5}$), 0),
 * (cos(2π/7), ±sin(2π/7), ±sin(π/7), ±sin(π/7)$\sqrt{(5+√5)/2}$),
 * (cos(2π/7), ±sin(2π/7), ±sin(π/7)(3+$\sqrt{5}$)/2, ±sin(π/7)$\sqrt{5+2√5}$),
 * (cos(2π/7), ±sin(2π/7), ±sin(π/7)(1+$\sqrt{5}$), 0),
 * (cos(4π/7), ±sin(4π/7), ±sin(π/7), ±sin(π/7)$\sqrt{(5+√5)/2}$),
 * (cos(4π/7), ±sin(4π/7), ±sin(π/7)(3+$\sqrt{5}$)/2, ±sin(π/7)$\sqrt{5+2√5}$),
 * (cos(4π/7), ±sin(4π/7), ±sin(π/7)(1+$\sqrt{5}$), 0),
 * (cos(6π/7), ±sin(6π/7), ±sin(π/7), ±sin(π/7)$\sqrt{(5+√5)/2}$),
 * (cos(6π/7), ±sin(6π/7), ±sin(π/7)(3+$\sqrt{5}$)/2, ±sin(π/7)$\sqrt{5+2√5}$),
 * (cos(6π/7), ±sin(6π/7), ±sin(π/7)(1+$\sqrt{5}$), 0).

Representations
A heptagonal-decagonal duoprism has the following Coxeter diagrams:


 * x7o x10o (full symmetry)
 * x5x x7o (decagons as dipentagons)