Let the patch of a partner in a protein complex be the collection of atoms accounting for the interaction. To improve our understanding of the structure–function relationship, we present a patch model decoupling the topological and geometric properties. While the geometry is classically encoded by the atomic positions, the topology is recorded in a graph encoding the relative position of concentric shells partitioning the interface atoms. The topological–geometric duality provides the basis of a generic dynamic programming-based algorithm comparing patches at the shell level, which may favor topological or geometric features. On the biological side, we address four questions, using 249 cocrystallized heterodimers organized in biological families. First, we dissect the morphology of binding patches and show that Nature enjoyed the topological and geometric degrees of freedom independently while retaining a finite set of qualitatively distinct topological signatures. Second, we argue that our shell-based comparison is effective to perform atomic-level comparisons and show that topological similarity is a less stringent than geometric similarity. We also use the topological versus geometric duality to exhibit topo-rigid patches, whose topology (but not geometry) remains stable upon docking. Third, we use our comparison algorithms to infer specificity-related information amidst a database of complexes. Finally, we exhibit a descriptor outperforming its contenders to predict the binding affinities of the affinity benchmark. The softwares developed with this article are available from http://team.inria.fr/abs/vorpatch_compatch/. Proteins 2012; © 2012 Wiley Periodicals, Inc.