The Regge symmetry, confocal conics, and the Schläfli formula
The Regge symmetry, confocal conics, and the Schläfli formula
The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here, we give a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic …