Stellated decachoron

The stellated decachoron is the simplest regular compound polychoron, and the third in an infinite series of bi-simplex compounds. It is a compound of two pentachora in dual orientation.

Vertex coordinates
The vertices of a regular pentachoron of edge length 1, centered at the origin, are given by:


 * $$\left(±\frac{1}{2},\,-\frac{\sqrt{3}}{6},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(0,\,\frac{\sqrt{3}}{3},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(0,\,0,\,\frac{\sqrt{6}}{4},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(0,\,0,\,0,\,\frac{\sqrt{10}}{5}\right).$$

And their opposites.