The main motivation here is a question: whether any polyhedron which can be subdivided into convex pieces without adding a vertex, and which has the same vertices as a convex polyhedron, is infinitesimally rigid. We prove that it is indeed the case for two classes of polyhedra: those obtained from a convex polyhedron by "denting" at most two edges at a common vertex, and suspensions with a natural subdivision. © 2009 Elsevier Ltd. All rights reserved.
Connelly, R., & Schlenker, J. M. (2010). On the infinitesimal rigidity of weakly convex polyhedra. European Journal of Combinatorics, 31(4), 1080–1090. https://doi.org/10.1016/j.ejc.2009.09.006