Reye configuration

Two regular tetrahedra may be inscribed within a cube, forming a stella octangula; these two tetrahedra are perspective figures to each other in four different ways, and the other four points of the configuration are their centers of perspectivity.

Any two disjoint spheres in three dimensional space, with different radii, have two bitangent double cones, the apexes of which are called the centers of similitude.

form the vertices of a 24-cell centered at the origin of four-dimensional Euclidean space.

The 12 axis lines can be grouped into 16 triples that lie in the same central plane of the 24-cell.

Each central plane intersects 6 vertices in the form of a regular hexagon.

Aravind (2000) pointed out that the Reye configuration underlies some of the proofs of the Bell–Kochen–Specker theorem about the non-existence of hidden variables in quantum mechanics.