Michael Floater has developed a linear method by convex combinations for the parameterization of polyhedral surfaces. He has shown the validity of the parameterization for triangulations, in other words, the one-to-one property of convex combination maps over triangulations. We have then extended the result to tillings. The resulting proof is a considerable simplification of Tutte's theory. We have then considered the extension of the result in the three-dimensional case: we have defined convex combination maps over tetrahedralizations and shown with a counterexample that these are not necessarily one-to-one. From this counterexample appears a necessary (maybe sufficient) condition for the map to be one-to-one and the current task is to establish sufficient conditions.