Heptagonal-octagonal duoprism

The heptagonal-octagonal duoprism or heodip, also known as the 7-8 duoprism, is a uniform duoprism that consists of 7 octagonal prisms and 8 heptagonal prisms, with two of each joining at each vertex.

Vertex coordinates
The coordinates of a heptagonal-octagonal duoprism, centered at the origin and with edge length 2sin(π/7), are given by:
 * (±sin(π/7), ±sin(π/7)(1+$\sqrt{2+√2}$), 1, 0),
 * (±sin(π/7), ±sin(π/7)(1+$\sqrt{2}$), cos(2π/7), ±sin(2π/7)),
 * (±sin(π/7), ±sin(π/7)(1+$\sqrt{2}$), cos(4π/7), ±sin(4π/7)),
 * (±sin(π/7), ±sin(π/7)(1+$\sqrt{2}$), cos(6π/7), ±sin(6π/7)),
 * (±sin(π/7)(1+$\sqrt{2}$), ±sin(π/7), 1, 0),
 * (±sin(π/7)(1+$\sqrt{2}$), ±sin(π/7), cos(2π/7), ±sin(2π/7)),
 * (±sin(π/7)(1+$\sqrt{2}$), ±sin(π/7), cos(4π/7), ±sin(4π/7)),
 * (±sin(π/7)(1+$\sqrt{2}$), ±sin(π/7), cos(6π/7), ±sin(6π/7)).

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


 * x7o x8o (full symmetry)
 * x4x x7o (octagons as ditetragons)