A new model of cell sorting based on a geometric representation (trivalent map) and its associated structure (triangulated graph) is presented. This model varies substantially from existing mathematical models in that individual cells are represented by variable n-gons, n [greater-or-equal, slanted] 3, whereas in current models cells are considered to be fixed (non-deformable) geometric, i.e. hexagonal or square objects. An exchange mechanism which operates on this graph is investigated and possible drivers are discussed.