Pentagonal-heptagrammic duoprism

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

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


 * (±sin(2π/7), -2sin(2π/7)$\sqrt{5}$, 1, 0),
 * (±sin(2π/7), -2sin(2π/7)$\sqrt{2}$, cos(2π/7), ±sin(2π/7)),
 * (±sin(2π/7), -2sin(2π/7)$\sqrt{(5+√5)/10+1/[4sin^{2}(2π/7)]}$, cos(4π/7), ±sin(4π/7)),
 * (±sin(2π/7), -2sin(2π/7)$\sqrt{5-2√5}$, cos(6π/7), ±sin(6π/7)),
 * (±(1+$\sqrt{(5+2√5)/20}$)sin(2π/7)/2, 2sin(2π/7)$\sqrt{(5+2√5)/20}$, 1, 0),
 * (±(1+$\sqrt{(5+2√5)/20}$)sin(2π/7)/2, 2sin(2π/7)$\sqrt{(5+2√5)/20}$, cos(2π/7), ±sin(2π/7)),
 * (±(1+$\sqrt{5}$)sin(2π/7)/2, 2sin(2π/7)$\sqrt{(5-√5)/40}$, cos(4π/7), ±sin(4π/7)),
 * (±(1+$\sqrt{5}$)sin(2π/7)/2, 2sin(2π/7)$\sqrt{(5-√5)/40}$, cos(6π/7), ±sin(6π/7)),
 * (0, 2sin(2π/7)$\sqrt{5}$, 1, 0),
 * (0, 2sin(2π/7)$\sqrt{(5-√5)/40}$, cos(2π/7), ±sin(2π/7)),
 * (0, 2sin(2π/7)$\sqrt{5}$, cos(4π/7), ±sin(4π/7)),
 * (0, 2sin(2π/7)$\sqrt{(5-√5)/40}$, cos(6π/7), ±sin(6π/7)).