Abstract
The well-known formula for finding the area of a triangle in terms of its sides is generalized to volumes of polyhedra in the following way. It is proved that for a polyhedron (with triangular faces) with a given combinatorial structure and with a given collection of edge lengths there is a polynomial such that the volume of the polyhedron is a root of it, and the coefficients of the polynomial depend only on and and not on the concrete configuration of the polyhedron itself. A number of problems in the metric theory of polyhedra are solved as a consequence.
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