Flexible polyhedra are a class of polyhedra that can undergo a continuous motion that preserves the shape of their faces. By Cauchy's rigidity theorem, they must be non-convex, and it is known (the "bellows theorem") that the volume of the polyhedron must stay constant throughout this motion. A stronger version of this theorem states that the Dehn invariant of such a polyhedron must also remain invariant throughout any continuous motion. This result is called the "strong bellows theorem". It has been proven for all non-self-intersecting flexible polyhedra.