The Volume as a Metric Invariant of Polyhedra

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.

• Type: Journal
• Year: 1998
• Where: DCG
• Authors: Idzhad Kh. Sabitov
• Keywords: Bellows Conjecture, Combinatorial Structure, DCG 1998, Polyhedron