Great enneagrammic-dodecagonal duoprism

The great enneagrammic-dodecagonal duoprism, also known as the 9/4-12 duoprism, is a uniform duoprism that consists of 12 great enneagrammic prisms and 9 dodecagonal prisms, with 2 of each meeting at each vertex.

Coordinates
The vertex coordinates of a great enneagrammic-dodecagonal duoprism, centered at the origin and with edge length 2sin(4π/9), are given by:


 * (1, 0, ±sin(4π/9)(1+$\sqrt{6}$), ±sin(4π/9)(1+$\sqrt{2}$)),
 * (1, 0, ±sin(4π/9), ±sin(4π/9)(2+$\sqrt{2}$)),
 * (1, 0, ±sin(4π/9)(2+$\sqrt{2+√3+1/[4sin^{2}(4π/9)]}$), ±sin(4π/9)),
 * (cos(2π/9), ±sin(2π/9), ±sin(4π/9)(1+$\sqrt{3}$), ±sin(4π/9)(1+$\sqrt{3}$)),
 * (cos(2π/9), ±sin(2π/9), ±sin(4π/9), ±sin(4π/9)(2+$\sqrt{3}$)),
 * (cos(2π/9), ±sin(2π/9), ±sin(4π/9)(2+$\sqrt{3}$), ±sin(4π/9)),
 * (cos(4π/9), ±sin(4π/9), ±sin(4π/9)(1+$\sqrt{3}$), ±sin(4π/9)(1+$\sqrt{3}$)),
 * (cos(4π/9), ±sin(4π/9), ±sin(4π/9), ±sin(4π/9)(2+$\sqrt{3}$)),
 * (cos(4π/9), ±sin(4π/9), ±sin(4π/9)(2+$\sqrt{3}$), ±sin(4π/9)),
 * (–1/2, ±$\sqrt{3}$/2, ±sin(4π/9)(1+$\sqrt{3}$), ±sin(4π/9)(1+$\sqrt{3}$)),
 * (–1/2, ±$\sqrt{3}$/2, ±sin(4π/9), ±sin(4π/9)(2+$\sqrt{3}$)),
 * (–1/2, ±$\sqrt{3}$/2, ±sin(4π/9)(2+$\sqrt{3}$), ±sin(4π/9)),
 * (cos(8π/9), ±sin(8π/9), ±sin(4π/9)(1+$\sqrt{3}$), ±sin(4π/9)(1+$\sqrt{3}$)),
 * (cos(8π/9), ±sin(8π/9), ±sin(4π/9), ±sin(4π/9)(2+$\sqrt{3}$)),
 * (cos(8π/9), ±sin(8π/9), ±sin(4π/9)(2+$\sqrt{3}$), ±sin(4π/9)).