Pentagrammic-heptagrammic duoprism

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

The name can also refer to the pentagrammic-great heptagrammic duoprism.

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


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