Geodesic
A generalized Heron--Tartaglia formula and some of its consequences
Sbornik. Mathematics, Tome 189 (1998) no. 10, pp. 1533-1561

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $K$ and with a given collection $(l)$ 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 $K$ and $(l)$ 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. 
@article{SM_1998_189_10_a5,
     author = {I. Kh. Sabitov},
     title = {A generalized {Heron--Tartaglia} formula and some of its consequences},
     journal = {Sbornik. Mathematics},
     pages = {1533--1561},
     publisher = {mathdoc},
     volume = {189},
     number = {10},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_10_a5/}
}
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I. Kh. Sabitov. A generalized Heron--Tartaglia formula and some of its consequences. Sbornik. Mathematics, Tome 189 (1998) no. 10, pp. 1533-1561. http://geodesic.mathdoc.fr/item/SM_1998_189_10_a5/