Pentagonal-heptagonal duoprism

The pentagonal-heptagonal duoprism or pheddip, also known as the 5-7 duoprism, is a uniform duoprism that consists of 5 heptagonal prisms, 7 pentagonal prisms and 35 vertices.

Coordinates
The vertex coordinates of a pentagonal-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)$\sqrt{(5+2√5)/5}$, cos(4π/7), ±sin(4π/7)),
 * (±sin(π/7), –sin(π/7)$\sqrt{(5+2√5)/5}$, cos(6π/7), ±sin(6π/7)),
 * (±sin(π/7)(1+$\sqrt{(5+2√5)/5}$)/2, sin(π/7)$\sqrt{(5+2√5)/5}$, 1, 0),
 * (±sin(π/7)(1+$\sqrt{5}$)/2, sin(π/7)$\sqrt{(5–√5)/10}$, cos(2π/7), ±sin(2π/7)),
 * (±sin(π/7)(1+$\sqrt{5}$)/2, sin(π/7)$\sqrt{(5–√5)/10}$, cos(4π/7), ±sin(4π/7)),
 * (±sin(π/7)(1+$\sqrt{5}$)/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)$\sqrt{(5+√5)/10}$, cos(4π/7), ±sin(4π/7)),
 * (0, 2sin(π/7)$\sqrt{(5+√5)/10}$, cos(6π/7), ±sin(6π/7)).