Great heptagrammic-dodecagrammic duoprism

The great heptagrammic-dodecagrammic duoprism, also known as the 7/3-12/5 duoprism, is a uniform duoprism that consists of 12 great heptagrammic prisms and 7 dodecagrammic prisms, with 2 of each meeting at each vertex.

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


 * (1, 0, ±sin(3π/7)($\sqrt{6}$–1), ±sin(3π/7)($\sqrt{2}$–1)),
 * (1, 0, ±sin(3π/7), ±sin(3π/7)(2–$\sqrt{2}$)),
 * (1, 0, ±sin(3π/7)(2–$\sqrt{3}$), ±sin(3π/7)),
 * (cos(2π/7), ±sin(2π/7), ±sin(3π/7)($\sqrt{3}$–1), ±sin(3π/7)($\sqrt{3}$–1)),
 * (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)($\sqrt{3}$–1), ±sin(3π/7)($\sqrt{3}$–1)),
 * (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)($\sqrt{3}$–1), ±sin(3π/7)($\sqrt{3}$–1)),
 * (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)).