Stellated decachoron

The stellated decachoron or sted is the simplest regular compound polychoron, and the third in an infinite series of regular bi-simplex compounds. It is a compound of two pentachora in dual orientations. It has 10 tetrahedra as cells, with 4 cells joinig at a vertex. As the name suggests, it is also a stellation of the uniform decachoron.

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


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