Three-dimensional point sets can be used to represent data in different domains. Given a database of 3D point sets, pattern discovery looks for similar subsets that occur in multiple point sets. Geometric hashing proved to be an effective technique in discovering patterns in 3D point sets. However, there are also known shortcomings. We propose a new indexing technique called \Delta B⁺ Trees. It is an extension of B⁺-Trees that stores point triplet information. It overcomes the shortcomings of the geometric hashing technique. We introduce four different ways of constructing the key from a triplet. We give analytical comparison between the new index structure and the geometric hashing technique. We also conduct experiments on both synthetic data and real data to evaluate the performance.