FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1996, VOLUME 2, NUMBER 4, PAGES 1235-1246

The volume of polyhedron as a function of its metric

I. Kh. Sabitov

Abstract

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It is proved that the volume of any polyhedron is root of some polynomial whose coefficients are not depending on the concrete form of the polyhedron in three-space under the condition that its metric is known a priori. As consequence we have a proof of the “bellows conjecture” affirming the invariance of volume of a flexible polyhedron in the process of its flexion.

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