Pentagonal-tetrahedral duoprism

The pentagonal-tetrahedral duoprism or petet is a convex uniform duoprism that consists of 5 tetrahedral prisms and 4 triangular-pentagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-pentagonal duoprisms.

Vertex coordinates
The vertices of a pentagonal-tetrahedral duoprism of edge length 1 are given by all even sign changes of the last three coordinates of:
 * $$\left(±\frac{1}{2},\, -\sqrt{\frac{5+2\sqrt{5}}{20}},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac{1+\sqrt{5}}{4},\, \sqrt{\frac{5-\sqrt{5}}{40}},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt{5}}{10}},\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$