Pentagonal duoprism

The pentagonal duoprism or pedip, also known as the pentagonal-pentagonal duoprism, the 5 duoprism or the 5-5 duoprism, is a noble uniform duoprism that consists of 10 pentagonal prisms and 25 vertices. It is also the 10-4 gyrochoron and the square funk prism.

Vertex coordinates
The vertices of a pentagonal duoprism of edge length 1, centered at the origin, are given by:
 * (0, $\sqrt{50+10√5}$/10, 0, $\sqrt{50+10√5}$/10)
 * (0, $\sqrt{50+10√5}$/10, ±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20)
 * (0, $\sqrt{50+10√5}$/10, ±1/2, –$\sqrt{25+10√5}$/10)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20, 0, $\sqrt{50+10√5}$/10)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20, ±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20)
 * (±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20, ±1/2, –$\sqrt{25+10√5}$/10)
 * (±1/2, –$\sqrt{25+10√5}$/10, 0, $\sqrt{50+10√5}$/10)
 * (±1/2, –$\sqrt{25+10√5}$/10, ±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20)
 * (±1/2, –$\sqrt{25+10√5}$/10, ±1/2, –$\sqrt{25+10√5}$/10)