Забавно, Адипразито тоже про жесткость многогранников пишет

https://arxiv.org/abs/1909.10794

Unstable blueprints can be shared
Karim Adiprasito
(Submitted on 24 Sep 2019 (v1), last revised 25 Sep 2019 (this version, v2))
This expository note illustrates toric perturbation and biased pairing theory to show that Artinian reductions of face rings of 2-spheres that do not satisfy the Lefschetz property can be cut along a flat equator. This complements classical work of Bricard and Connelly, and exhibits a fundamental symmetry in non-rigid triangulations of spheres.