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Discrete & Computational Geometry

, Volume 20, Issue 4, pp 405–425 | Cite as

The Volume as a Metric Invariant of Polyhedra

  • I. Kh. Sabitov

Abstract.

It is proved that in R 3 the volume of any polyhedron is a root of some polynomial with coefficients depending only on the combinatorial structure and the metric of the polyhedron. As a consequence, we have a proof of the ``bellows conjecture'' affirming the invariance of the volume of a flexible polyhedron in the process of its flexion.

Keywords

Combinatorial Structure Flexible Polyhedron 
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Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • I. Kh. Sabitov
    • 1
  1. 1.Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119899 Russia matan@nss.msu.suRU

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