Heptagonal-dodecagonal duoprism

The heptagonal-dodecagonal duoprism or hetwadip, also known as the 7-12 duoprism, is a uniform duoprism that consists of 7 dodecagonal prisms and 12 heptagonal prisms, with two of each joining at each vertex.

Vertex coordinates
The coordinates of a heptagonal-dodecagonal duoprism, centered at the origin and with edge length 2sin(π/7), are given by:
 * (1, 0, ±sin(π/7)(1+$\sqrt{2}$), ±sin(π/7)(1+$\sqrt{6}$)),
 * (1, 0, ±sin(π/7), ±sin(π/7)(2+$\sqrt{2}$)),
 * (1, 0, ±sin(π/7)(2+$\sqrt{3}$), ±sin(π/7)),
 * (cos(2π/7), ±sin(2π/7), ±sin(π/7)(1+$\sqrt{3}$), ±sin(π/7)(1+$\sqrt{3}$)),
 * (cos(2π/7), ±sin(2π/7), ±sin(π/7), ±sin(π/7)(2+$\sqrt{3}$)),
 * (cos(2π/7), ±sin(2π/7), ±sin(π/7)(2+$\sqrt{3}$), ±sin(π/7)),
 * (cos(4π/7), ±sin(4π/7), ±sin(π/7)(1+$\sqrt{3}$), ±sin(π/7)(1+$\sqrt{3}$)),
 * (cos(4π/7), ±sin(4π/7), ±sin(π/7), ±sin(π/7)(2+$\sqrt{3}$)),
 * (cos(4π/7), ±sin(4π/7), ±sin(π/7)(2+$\sqrt{3}$), ±sin(π/7)),
 * (cos(6π/7), ±sin(6π/7), ±sin(π/7)(1+$\sqrt{3}$), ±sin(π/7)(1+$\sqrt{3}$)),
 * (cos(6π/7), ±sin(6π/7), ±sin(π/7), ±sin(π/7)(2+$\sqrt{3}$)),
 * (cos(6π/7), ±sin(6π/7), ±sin(π/7)(2+$\sqrt{3}$), ±sin(π/7)).

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


 * x7o x12o (full symmetry)
 * x6x x7o (dodecagons as dihexagons)