Skew compound of four triangles (chiral cubic symmetry)

The  is a regular skew compound polygon made of four triangles.

Vertex coordinates
The has the same vertices as a cuboctahedron. With unit side length vertex coordinates are given by all permutations of
 * $$\left(\pm\frac1{\sqrt6},\,\pm\frac1{\sqrt6},\,0\right)$$