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. Together with its dual, it is the first in an infinite family of pentagonal dihedral swirlchora.

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