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The equilibrium conditions impose nontrivial geometrical constraints on theconfigurations that a two-dimensional foam can attain. In the first place, thethree centers of the films that converge to a vertex have to be on a line, i.e.all vertices are aligned. Moreover an equilibrated foam must admit a reciprocalfigure. This means that it must be possible to find a set of points P_i on theplane, one per bubble, such that the segments (P_i P_j) are normal to thecorresponding foam films. It is furthermore shown that these constraints areequivalent to the requirement that the foam be a Sectional MultiplicativeVoronoi Partition (SMVP). A SMVP is a cut with a two-dimensional plane, of athree-dimensional Multiplicative Voronoi Partition. Thus given an arbitraryequilibrated foam, we can always find point-like sources (one per bubble) inthree dimensions that reproduce this foam as a generalized Voronoi partition.These sources are the only degrees of freedom that we need in oder to fullydescribe the foam.Comment: RevTeX + epsfig, 19 pages + 19 eps figure

Geometrical consequences of foam equilibrium