Bellows conjecture for flexible polyhedra

Let $P$ be a flexible polyhedron in Euclidean space, and let its generalized volume be the volume invariant associated with its possibly self-intersecting realization. A bending is a continuous flex of $P$ preserving the lengths of its edges. Bellows conjecture. The generalized volume of a flexible polyhedron does not change when it is bending. This conjecture concerns volume invariance under flexing; the preceding Sabitov theorem allows it to be proved for Euclidean polyhedra.