## 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)

### Keywords:

volume; polyhedron; metric