The generalized bellows conjecture for flexible polyhedra in Euclidean space

Let $P\colon K\to\mathbb{R}^n$ be a flexible, not necessarily embedded polyhedron, and let $V_K(P)$ denote its generalized oriented volume, defined by integrating its characteristic function over $\mathbb{R}^n$. The generalized bellows conjecture. For $n\ge 3$, the generalized oriented volume of any flexible polyhedron in $\mathbb{R}^n$ is constant during the flexion. This generalizes the three-dimensional bellows conjecture to arbitrary flexible, possibly self-intersecting polyhedra and higher dimensions; its resolution is not specified in the supplied text.