Approximate geometric models, e.g. as created by reverse engineering, describe the approximate shape of an object, but do not record the underlying design intent. Automatically inferring geometric aspects of the design intent, represented by feature trees and geometric constraints, enhances the utility of such models for downstream tasks. One approach to design intent detection in such models is to decompose them into regularity features. Geometric regularities such as symmetries may then be sought in each regularity feature, and subsequently be combined into a global, consistent description of the model’s geometric design intent. This paper describes a systematic approach for finding such regularity features based on recovering broken symmetries in the model. The output is a tree of regularity features for subsequent use in regularity detection and selection. Experimental results are given to demonstrate the operation and efficiency of the algorithm.