The strong stress-flex conjecture for coned polytope frameworks

Let $P$ be any “polytope” with a full-dimensional affine span in $\mathbb R^d$. Let $\mathbf p_{n+1}$ be placed anywhere in $\mathbb R^d$. Let $\Omega$ be any stress for the bar framework obtained by coning the one-skeleton of $P$ over $\mathbf p_{n+1}$, and let $\hat{\mathbf p}'$ be any infinitesimal flex of the bar framework. The strong stress-flex conjecture. The stress-flex condition holds; that is, the last row of $\Omega\hat{\mathbf p}'$ equals zero. The authors report that numerical experiments support this stronger formulation, including examples with cone points outside the polytope, non-convex and non-embedded polyhedra, higher-genus and non-orientable polyhedra, and the hypercube in $\mathbb R^4$, but no proof or resolution is given here.