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The volume of a polyhedron as a function of its metric. (Russian. English summary) Zbl 0904.52002

Summary: It is proved that the volume of any polyhedron is the 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 the volume of a flexible polyhedron in the process of its flexion.

MSC:

52A10 Convex sets in \(2\) dimensions (including convex curves)
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