Heptagrammic-dodecagrammic duoprism

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

The name can also refer to the great heptagrammic-dodecagrammic duoprism.

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


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