Protein-protein interactions, which form the basis for most cellular processes, result in the formation of protein interfaces. Believing that the local shape of proteins is crucial, we take a geometric approach and present a definition of an interface surface formed by two or more proteins. We also present an algorithm and study the geometric and topological properties of these surfaces, thus paving the way for future biochemical studies of protein-protein interactions. Categories and Subject Descriptors I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling -- geometric algorithms; J.2 [Computer Applications]: Physical Sciences and Engineering -- chemistry, physics; J.3 [Computer Applications]: Life and Medical Sciences -- biology and genetics. General Terms Algorithms, Theory. Keywords Protein interaction, interface surfaces, geometric and topological algorithms, Voronoi diagrams, filtrations.