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On the infinitesimal rigidity of weakly convex polyhedra

Robert Connelly·Jean-Marc Schlenker
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Abstract

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.

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Robert Connelly, Jean-Marc Schlenker. 2006-06-30. On the infinitesimal rigidity of weakly convex polyhedra. https://arxiv.org/abs/math/0606681

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