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Feature selection methods that exploit spatiotemporal data structures are rare. Spatiotemporal feature importance measures are even rarer. We propose a set of feature importance scores that give insights into the spatial, temporal and variable dimensions of spatiotemporal datasets. To this end, we systematically aggregate feature importance scores of reduced models that were trained on dices of the spatiotemporal hypercube. The scores can be calculated from regression coefficients, or from any other upstream feature importance metric. In an extensive case study, we apply the developed methods to a challenging solar power forecasting task, demonstrating their effectiveness in a field closely related to energy meteorology, which is widely recognized as highly complex.