A method is proposed for rapidly, quantitatively comparing protein structures of arbitrary sizes, based on the differential geometric representation. The method is applied to a group of 22 protein x-ray structures, and the resulting network of closest relationships is delineated. Several well-known fold types are automatically detected as groupings of related structures, even when the constituent proteins are of different lengths. A complete gradation of types is shown to be detected, ranging from all-helical to all-beta-structure proteins. A relationship among functionally similar proteins is shown in several cases, even where their three-dimensional structures differ. It is suggested that the positions of proteins within the network of relationships correspond with their folding mechanisms.