The bellows conjecture for flexible polyhedra in Euclidean space

A flexor is a flexible polyhedron in $\mathbb{R}^3$, and a flexion is a continuous deformation preserving its combinatorial type and the shapes of its faces. The bellows conjecture. The volume of any flexor in $\mathbb{R}^3$ is constant during the flexion. The conjecture arose from the observation that the volumes of the first known flexible polyhedra remained constant during flexion; its higher-dimensional and non-Euclidean generalisations are stated separately in the source.