Stellated icositetrachoron

The stellated icositetrachoron or stico is a regular compound polychoron. It is a compound of three hexadecachora. It has 48 tetrahedra as cells which lie in pairs in the same hyperplane, so they combine into 24 stella octangulas. 8 cells join at each vertex.

Vertex coordinates
The vertices of a stellated icositetrachoron of edge length 1, centered at the origin, are given by all permutations of:
 * $$\left(±\frac12,\,±\frac12,\,0,\,0\right).$$

The same stellated icositetrachoron in opposite orientation to this one has vertices given by all permutations of:
 * $$\left(±\frac{\sqrt2}{4},\,±\frac{\sqrt2}{4},\,±\frac{\sqrt2}{4},\,±\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,0\right).$$