Great enneagrammic-decagonal duoprism

The great enneagrammic-decagonal duoprism, also known as gistdedip or the 9/4-10 duoprism, is a uniform duoprism that consists of 10 great enneagrammic prisms and 9 decagonal prisms, with 2 of each meeting at each vertex.

Vertex coordinates
The coordinates of a great enneagrammic-decagonal duoprism, centered at the origin and with edge length 2sin(4π/9), are given by:
 * (1, 0, ±sin(4π/9), ±sin(4π/9)$\sqrt{(5+√5)/2}$),
 * (1, 0, ±sin(4π/9)(3+$\sqrt{2}$)/2, ±sin(4π/9)$\sqrt{5+2√5}$),
 * (1, 0, ±sin(4π/9)(1+$\sqrt{5}$), 0),
 * (cos(2π/9), ±sin(2π/9), ±sin(4π/9), ±sin(4π/9)$\sqrt{(5+√5)/2}$),
 * (cos(2π/9), ±sin(2π/9), ±sin(4π/9)(3+$\sqrt{5}$)/2, ±sin(4π/9)$\sqrt{5+2√5}$),
 * (cos(2π/9), ±sin(2π/9), ±sin(4π/9)(1+$\sqrt{5}$), 0),
 * (cos(4π/9), ±sin(4π/9), ±sin(4π/9), ±sin(4π/9)$\sqrt{(5+√5)/2}$),
 * (cos(4π/9), ±sin(4π/9), ±sin(4π/9)(3+$\sqrt{5}$)/2, ±sin(4π/9)$\sqrt{5+2√5}$),
 * (cos(4π/9), ±sin(4π/9), ±sin(4π/9)(1+$\sqrt{5}$), 0),
 * (–1/2, ±$\sqrt{(5+√5)/2}$/2, ±sin(4π/9), ±sin(4π/9)$\sqrt{5}$),
 * (–1/2, ±$\sqrt{3}$/2, ±sin(4π/9)(3+$\sqrt{5+2√5}$)/2, ±sin(4π/9)$\sqrt{3}$),
 * (–1/2, ±$\sqrt{5}$/2, ±sin(4π/9)(1+$\sqrt{(5+√5)/2}$), 0),
 * (cos(8π/9), ±sin(8π/9), ±sin(4π/9), ±sin(4π/9)$\sqrt{3}$),
 * (cos(8π/9), ±sin(8π/9), ±sin(4π/9)(3+$\sqrt{5}$)/2, ±sin(4π/9)$\sqrt{5+2√5}$),
 * (cos(8π/9), ±sin(8π/9), ±sin(4π/9)(1+$\sqrt{5}$), 0).