  Determining the number of embeddings of Laman graph frameworks is an open
problem which corresponds to understanding the solutions of the resulting
systems of equations. In this paper we investigate the bounds which can be
obtained from the viewpoint of Bernstein's Theorem. The focus of the paper is
to provide the methods to study the mixed volume of suitable systems of
polynomial equations obtained from the edge length constraints. While in most
cases the resulting bounds are weaker than the best known bounds on the number
of embeddings, for some classes of graphs the bounds are tight.
