This paper presents a method for efficiently maintaining and searching a database of three-dimensional models so they can be reliable recognized from arbitrary two-dimensional projections in the presence of noise and occlusion. The core of the process is the topologically-defined network of invariants which breaks three-dimensional models down into small, local groups of features and indexes these groups using translation, rotation, scaling, and orthographic projection invariant functions. The network encodes the geometrical relationships between these groups so that grouping information can be used to increase the speed of matching.