Generic projective rigidity conjecture for convex polytopes

Let $P\subset\mathbb{R}^d$ be a convex polytope of dimension $d\geq 3$. A projective transformation is generic when it avoids the exceptional algebraic conditions relevant to the rigidity property. Generic projective rigidity conjecture. A generic projective transformation of $P$ is (first-order) rigid. This proposed approach is motivated by the fact that the known flexible polytopes have parallel edges, whereas a generic projective transformation has no parallel edges. Whether this implication yields rigidity in all dimensions is not established in the paper.