Pentagonal-great enneagrammic duoprism

The pentagonal-great enneagrammic duoprism, also known as the 5-9/4 duoprism, is a uniform duoprism that consists of 9 pentagonal prism s and 5 great enneagrammic prism s, with 2 of each meeting at each vertex.

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


 * (±sin(4π/9), –sin(4π/9)$\sqrt{5}$, 1, 0),
 * (±sin(4π/9), –sin(4π/9)$\sqrt{2}$, cos(2π/9), ±sin(2π/9)),
 * (±sin(4π/9), –sin(4π/9)$\sqrt{(5+√5)/10+1/[4sin^{2}(4π/9)]}$, cos(4π/9), ±sin(4π/9)),
 * (±sin(4π/9), –sin(4π/9)$\sqrt{5+2√5}$, –1/2, ±√3/2),
 * (±sin(4π/9), –sin(4π/9)$\sqrt{(5+2√5)/5}$, cos(8π/9), ±sin(8π/9)),
 * (±(1+$\sqrt{(5+2√5)/5}$)sin(4π/9)/2, sin(4π/9)$\sqrt{(5+2√5)/5}$, 1, 0),
 * (±(1+$\sqrt{(5+2√5)/5}$)sin(4π/9)/2, sin(4π/9)$\sqrt{(5+2√5)/5}$, cos(2π/9), ±sin(2π/9)),
 * (±(1+$\sqrt{5}$)sin(4π/9)/2, sin(4π/9)$\sqrt{(5-√5)/10}$, cos(4π/9), ±sin(4π/9)),
 * (±(1+$\sqrt{5}$)sin(4π/9)/2, sin(4π/9)$\sqrt{(5-√5)/10}$, –1/2, ±√3/2),
 * (±(1+$\sqrt{5}$)sin(4π/9)/2, sin(4π/9)$\sqrt{(5-√5)/10}$, cos(8π/9), ±sin(8π/9)),
 * (0, 2sin(4π/9)$\sqrt{5}$, 1, 0),
 * (0, 2sin(4π/9)$\sqrt{(5-√5)/10}$, cos(2π/9), ±sin(2π/9)),
 * (0, 2sin(4π/9)$\sqrt{5}$, cos(4π/9), ±sin(4π/9)),
 * (0, 2sin(4π/9)$\sqrt{(5-√5)/10}$, –1/2, ±√3/2),
 * (0, 2sin(4π/9)$\sqrt{(5+√5)/10}$, cos(8π/9), ±sin(8π/9)).