MOTIVATION: As the number of experimentally solved protein structures rises, it becomes increasingly appealing to use structural information for predictive tasks involving proteins. Due to the large variation in protein sizes, folds and topologies, an attractive approach is to embed protein structures into fixed-length vectors, which can be used in machine learning algorithms aimed at predicting and understanding functional and physical properties. Many existing embedding approaches are alignment based, which is both time-consuming and ineffective for distantly related proteins. On the other hand, library- or model-based approaches depend on a small library of fragments or require the use of a trained model, both of which may not generalize well. RESULTS: We present Geometricus, a novel and universally applicable approach to embedding proteins in a fixed-dimensional space. The approach is fast, accurate, and interpretable. Geometricus uses a set of 3D moment invariants to discretize fragments of protein structures into shape-mers, which are then counted to describe the full structure as a vector of counts. We demonstrate the applicability of this approach in various tasks, ranging from fast structure similarity search, unsupervised clustering and structure classification across proteins from different superfamilies as well as within the same family. AVAILABILITY AND IMPLEMENTATION: Python code available at https://git.wur.nl/durai001/geometricus.