Pentagonal-truncated cubic duoprism

The pentagonal-truncated cubic duoprism or petic is a convex uniform duoprism that consists of 5 truncated cubic prisms, 6 pentagonal-octagonal duoprisms and 8 triangular-pentagonal duoprisms.

Vertex coordinates
The vertices of a pentagonal-truncated cubic duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of:
 * (0, $\sqrt{225+10√205+20√10}$/10, 1/2, (1+$\sqrt{50+10√5}$)/2, (1+$\sqrt{2}$)/2)
 * (±(1+$\sqrt{2}$)/4, $\sqrt{5}$/20, 1/2, (1+$\sqrt{50–10√5}$)/2, (1+$\sqrt{2}$)/2)
 * (±1/2, –$\sqrt{2}$/10, 1/2, (1+$\sqrt{25+10√5}$)/2, (1+$\sqrt{2}$)/2)