Pentagrammic tegum

The pentagrammic tegum is a star polyhedron. It can be constructed as the dual of the pentagrammic prism or as the tegum product of the pentagram and a line segment.

Vertex coordinates
A pentagrammic tegum of edge length 1 has the following vertices:


 * $$\left(±\frac{1}{2},\, -\sqrt{\frac{5-2\sqrt{5}}{20}},\,0\right),$$
 * $$\left(±\frac{\sqrt{5}-1}{4},\, \sqrt{\frac{5+\sqrt{5}}{40}},\,0\right),$$
 * $$\left(0,\, \sqrt{\frac{5-\sqrt{5}}{10}},\,0\right),$$
 * $$\left(0,\,0,\,±\sqrt{\frac{5+\sqrt5}{10}}\right).$$