  The equilibrium conditions impose nontrivial geometrical constraints on the
configurations that a two-dimensional foam can attain. In the first place, the
three 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 reciprocal
figure. This means that it must be possible to find a set of points P_i on the
plane, one per bubble, such that the segments (P_i P_j) are normal to the
corresponding foam films. It is furthermore shown that these constraints are
equivalent to the requirement that the foam be a Sectional Multiplicative
Voronoi Partition (SMVP). A SMVP is a cut with a two-dimensional plane, of a
three-dimensional Multiplicative Voronoi Partition. Thus given an arbitrary
equilibrated foam, we can always find point-like sources (one per bubble) in
three dimensions that reproduce this foam as a generalized Voronoi partition.
These sources are the only degrees of freedom that we need in oder to fully
describe the foam.
