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. It is the first in an infinite family of isogonal pentagonal dihedral swirlchora and also the first in an infinite family of isochoric pentagonal hosohedral 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+$\sqrt{(5+2√5)/20}$)/4, $\sqrt{5}$/20),
 * (0, $\sqrt{50+10√5}$/10, ±1/2, –$\sqrt{50+10√5}$/10),
 * (±(1+$\sqrt{50+10√5}$)/4, $\sqrt{5}$/20, 0, $\sqrt{50–10√5}$/10),
 * (±(1+$\sqrt{50+10√5}$)/4, $\sqrt{25+10√5}$/20, ±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20),
 * (±(1+$\sqrt{50+10√5}$)/4, $\sqrt{5}$/20, ±1/2, –$\sqrt{50–10√5}$/10),
 * (±1/2, –$\sqrt{5}$/10, 0, $\sqrt{50–10√5}$/10),
 * (±1/2, –$\sqrt{5}$/10, ±(1+$\sqrt{50–10√5}$)/4, $\sqrt{25+10√5}$/20),
 * (±1/2, –$\sqrt{25+10√5}$/10, ±1/2, –$\sqrt{50+10√5}$/10).