AbstractWe introduce a new model of proteins that extends and enhances the traditional graphical representation by associating a combinatorial object called a fatgraph to any protein based upon its intrinsic geometry. Fatgraphs can easily be stored and manipulated as triples of permutations, and these methods are therefore amenable to fast computer implementation. Applications include the refinement of structural protein classifications and the prediction of geometric and other properties of proteins from their chemical structures. © 2010 Wiley Periodicals, Inc.