Pentagonal-octagonal duoprism

The pentagonal-octagonal duoprism or podip, also known as the 5-8 duoprism, is a uniform duoprism that consists of 5 octagonal prisms, 8 pentagonal prisms and 40 vertices.

Vertex coordinates
Coordinates for the vertices of a pentagonal-octagonal duoprism with edge length 1 are given by:
 * (0, $\sqrt{5}$, ±1/2, ±(1+$\sqrt{2+√2}$)/2),
 * (0, $\sqrt{2}$, ±(1+$\sqrt{(15+5√2+√5)/10}$)/2, ±1/2),
 * (±(1+$\sqrt{75+50√2+10√80+60√5}$)/4, $\sqrt{(5+√5)/10}$, ±1/2, ±(1+$\sqrt{2}$)/2),
 * (±(1+$\sqrt{(5+√5)/10}$)/4, $\sqrt{2}$, ±(1+$\sqrt{5}$)/2, ±1/2),
 * (±1/2, –$\sqrt{(5+√5)/40}$, ±1/2, ±(1+$\sqrt{2}$)/2),
 * (±1/2, –$\sqrt{5}$, ±(1+$\sqrt{(5+√5)/40}$)/2, ±1/2).