Motivation: Clustering protein structures is an important task in structural bioinformatics. De novo structure prediction, for example, often involves a clustering step for nding the best prediction. Other applications include assigning proteins to fold families and analyzing molecular dynamics trajectories. Results: We present Pleiades, a novel approach to clustering protein structures with a rigorous mathematical underpinning. The method approximates clustering based on the root mean square deviation by rst mapping structures to Gauss integral vectors – which were introduced by Røgen and co-workers – and subsequently performing K-means clustering. Conclusions: Compared to current methods, Pleiades dramatically improves on the time needed to perform clustering, and can cluster a signicantly larger number of structures, while providing state-ofthe- art results. The number of low energy structures generated in a typical folding study, which is in the order of 50,000 structures, can be clustered within seconds to minutes.