Great icositetrachoron

The great icositetrachoron or gico is a regular compound polychoron. It is a compound of three tesseracts.

Vertex coordinates
The vertices of a great icositetrachoron of edge length 1, centered at the origin, are given by all permutations of:
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0\right).$$

The same great icositetrachoron in opposite orientation to this one has vertices given by all permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±1,\,0,\,0,\,0\right).$$