Heptagonal-dodecagrammic duoprism

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

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


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