There has been considerable interest in the physical basis for the increased thermostability of thermophilic proteins with respect to their mesophilic counterparts since the discovery of highly heat tolerant organisms. We have systematically studied several large sets of protein structures in order to find those properties with the most power to discriminate mesophilic proteins from their thermophilic orthologs and then to classify proteins based on sequence and structural properties. Most of the structure-based descriptors used in our discrimination and classification experiments were derived from the Delaunay tessellations of the protein structures