The Regge symmetry is a scissors congruence in hyperbolic space

Abstract

We give a constructive proof that the Regge symmetry is a scissors congruence in hyperbolic space. The main tool is Leibon’s construction for computing the volume of a general hyperbolic tetrahedron. The proof consists of identifying the key elements in Leibon’s construction and permuting them. AMS Classification 51M10; 51M20 

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