Abstract
New proofs are given for Cauchy's and Alexandrov's classical theorems on the rigidity of polyhedral frameworks, as well as their higher dimensional generalizations. Through duality, the rigidity of these frameworks follows from characterizations of the case of equality in Minkowski's quadratic inequality.
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Filliman, P. Rigidity and the Alexandrov-Fenchel inequality. Monatshefte für Mathematik 113, 1–22 (1992). https://doi.org/10.1007/BF01299302
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DOI: https://doi.org/10.1007/BF01299302