Great heptagrammic-dodecagonal duoprism

The great heptagrammic-dodecagonal duoprism, also known as the 7/3-12 duoprism, is a uniform duoprism that consists of 12 great heptagrammic prisms and 7 dodecagonal prisms, with 2 of each meeting at each vertex.

Coordinates
The vertex coordinates of a great heptagrammic-dodecagonal duoprism, centered at the origin and with edge length 2sin(3π/7), are given by:


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