Great icositetrachoron

The great icositetrachoron or gico is a regular compound polychoron. It is a compound of three tesseracts. It has 24 cubes as cells, with 8 cells joining at a vertex.

This compound has fissary vertices, with each vertex being used in two components and a compound (the stella octangula) for a vertex figure.

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:
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±1,\,0,\,0,\,0\right).$$

These are identical to those of a regular icositetrachoron, with which this compound shares its vertices and edges.