The Regge symmetry is a scissors congruence in hyperbolic space (Q1860327)

The paper gives a constructive proof that the Regge symmetry is a scissors congruence in hyperbolic \(3\)-space. The group of Regge symmetries of a tetrahedron consists of linear transformations on its six edges (representing the dihedral angles). The main result says that, in hyperbolic \(3\)-space, any two tetrahedra obtained from a given tetrahedron under a Regge symmetry are scissors congruent.