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On the infinitesimal rigidity of weakly convex polyhedra

2006/06/27 by Robert Connelly, Jean-Marc Schlenker, Jean‐Marc Schlenker +2
Engineering · Mathematics · #Advanced Materials and Mechanics #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.DG

paper · pdf · doi:10.48550/arxiv.math/0606681

v2: same as v1 but with 2 figures

arxiv created 2006/06/30 · arxiv updated 2009/12/01

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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