It is proved that in R3 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.
CITATION STYLE
Sabitov, I. K. (1998). The volume as a metric invariant of polyhedra. Discrete and Computational Geometry, 20(4), 405–425. https://doi.org/10.1007/PL00009393
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