Generic first-order rigidity conjecture for combinatorial types of convex polytopes

Let $\mathcal P$ be the combinatorial type of a convex polytope of dimension $d\geq 3$. Generic first-order rigidity conjecture. If $\mathcal P$ is the combinatorial type of a convex polytope of dimension $d\geq 3$, then $\mathcal P$ is generically (first-order) rigid. This is the precise formulation of generic rigidity used in the paper. The conjecture is proved for $d=3$, whereas it remains open for $d\geq 4$.