Cauchy's Rigidity Theorem (Convex Polyhedra)

Cauchy's Rigidity Theorem states that if two convex polyhedra have corresponding faces that are congruent to one another, then the two polyhedra must themselves be congruent, meaning a convex polyhedron cannot be flexed into a different shape while every one of its faces stays rigid. Named for Augustin-Louis Cauchy, it stands in contrast to non-convex polyhedra, some of which were later shown to flex continuously while preserving every face, a phenomenon Cauchy's own proof does not permit for the convex case.