  This is a study on approximating a Riemannian manifold by polyhedra. Our
scope is understanding Tullio Regge's [52] article in the restricted Riemannian
frame. We give a proof of the Regge theorem along lines close to its original
intuition: one can approximate a compact domain of a Riemannian manifold by
polyhedra in such a way that the integral of the scalar curvature is
approximated by a corresponding polyhedral curvature.
