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This paper proposes CREAM, a new explainable clustering technique based on decision tree induction, providing human-interpretable clusters by performing hypercubic approximations of the input feature space. CREAM may also be applied to data sets describing classification and regression tasks, given that the algorithm discriminates amongst input and output features. We also present OrCHiD, an automated tuning procedure to select the optimum CREAM parameter. Experiments demonstrating the effectiveness of CREAM in clustering, classification, and regression tasks are reported here, in comparison with other state-of-the-art techniques used as benchmarks.