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Online Analytical Processing (OLAP) systems allow one to quickly provide answers to analytical queries on multidimensional data. These systems are typically based on visualisations characterised by limited interaction and exploration capabilities. In this paper, we propose innovative visual and interaction techniques for the analysis of multidimensional data. The proposed solution is based on three-dimensional hypercube representations that can be explored using dynamic queries and that combines colour-coding, detail-on-demand, cutting planes and viewpoint control techniques. We demonstrate the effectiveness of our visualisation tool by providing some practical examples showing how it has been used for extracting information from real multidimensional data.