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See detailOn the infinitesimal rigidity of weakly convex polyhedra
Connelly, Robert; Schlenker, Jean-Marc UL

in European Journal of Combinatorics (2010), 31(4), 1080--1090

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 ... [more ▼]

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. [less ▲]

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