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The bellows conjecture (following I. Sabitov). (La conjecture des soufflets (d’après I. Sabitov).) (French) Zbl 1078.52014

Bourbaki seminar. Volume 2002/2003. Exposes 909–923. Paris: Société Mathématique de France (ISBN 2-85629-156-2/pbk). Astérisque 294, 77-95, Exp. No. 912 (2004).
This paper presents an overview of results connected with the famous bellows conjecture. The author addresses the issue of rigidity, infinitesimal rigidity and flexibility of polyhedral structures. He gives an interesting and clear summary of some of the proofs for the most important results in this field. This ranges from results by A.M. Legendre and A.L. Cauchy to recent results by I. Sabitov. The paper can be viewed as an excellent opportunity to get to know the state of the art in this interesting field.
For the entire collection see [Zbl 1052.00010].

MSC:

52C25 Rigidity and flexibility of structures (aspects of discrete geometry)
53A17 Differential geometric aspects in kinematics
51M04 Elementary problems in Euclidean geometries
51M09 Elementary problems in hyperbolic and elliptic geometries
51M20 Polyhedra and polytopes; regular figures, division of spaces
52B15 Symmetry properties of polytopes
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