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Rigidity and the Alexandrov-Fenchel inequality. (English) Zbl 0765.52017

New proofs are given for Cauchy’s and Alexandrov’s classical theorem 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.
Reviewer: P.Filliman

MSC:

52C25 Rigidity and flexibility of structures (aspects of discrete geometry)
52B11 \(n\)-dimensional polytopes
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
52A39 Mixed volumes and related topics in convex geometry
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References:

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