Shape of spinfoams encoded in graphs

As the EPRL model was evolving into its present form, a precise identification of the family of complexes (foams) used in the definition of the spinfoams has been abandoned. Most often mentioned possibilities were: simplicial complexes, linear complexes or locally linear complexes. We have solved that problem and we present a new compact characterization of a general foam. Our characterization leads also to a new type of diagrammatic notation directly from which a spinfoam amplitude can be written. This allows one to consider the diagrammatic notation as an alternative to standard 2-complex approach.