Connelly's Strong Bellows Conjecture for flexible polyhedra

Let $P$ be a flexible polyhedron in one of the constant-curvature spaces $\mathbb{E}^n$, $\mathbb{S}^n$, or $\mathbbl{\Lambda}^n$. Two polyhedra are scissors congruent if they can be divided into finitely many convex polytopes with pairwise disjoint interiors whose corresponding pieces are congruent. Connelly's Strong Bellows Conjecture. Any flexible polyhedron remains scissors congruent to itself during the flexion. Scissors congruence is stronger than equality of volume and is tied to Dehn invariants and Hilbert's Third Problem; the supplied source gives no resolution of this conjecture.