Pentagonal-truncated tetrahedral duoprism

The pentagonal-truncated tetrahedral duoprism or petut is a convex uniform duoprism that consists of 5 truncated tetrahedral prisms, 4 pentagonal-hexagonal duoprisms and 4 triangular-pentagonal duoprisms.

Vertex coordinates
The vertices of a pentagonal-truncated tetrahedral duoprism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of:
 * (0, $\sqrt{750+40√5}$/10, $\sqrt{50+10√5}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)
 * (±(1+$\sqrt{2}$)/4, $\sqrt{5}$/20, $\sqrt{50–10√5}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)
 * (±1/2, –$\sqrt{2}$/10, $\sqrt{25+10√5}$/4, $\sqrt{2}$/4, 3$\sqrt{2}$/4)