Pentagrammic-heptagonal duoprism

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

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


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