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Existing approaches usually perform spatiotemporal representation in the spatial and temporal dimensions, respectively, which isolates the spatial and temporal natures of the target and leads to sub-optimal embeddings. Neuroscience research has shown that the mammalian brain entorhinal-hippocampal system provides efficient graph representations for general knowledge. Moreover, entorhinal grid cells present concise spatial representations, while hippocampal place cells represent perception conjunctions effectively. Thus, the entorhinal-hippocampal system provides a novel angle for spatiotemporal representation, which inspires us to propose the SpatioTemporal aware Embedding framework (STE) and apply it to POIs (STEP). STEP considers two types of POI-specific representations: sequential representation and spatiotemporal conjunctive representation, learned using sparse unlabeled data based on the proposed graph-building policies. Notably, STEP jointly represents the spatiotemporal natures of POIs using both observations and contextual information from integrated spatiotemporal dimensions by constructing a spatiotemporal context graph. Furthermore, we introduce a successive POI recommendation method using STEP, which achieves state-of-the-art performance on two benchmarks. In addition, we demonstrate the excellent performance of the STE representation approach in other spatiotemporal representation-centered tasks through a case study of the traffic flow prediction problem. Therefore, this work provides a novel solution to spatiotemporal representation and paves a new way for spatiotemporal modeling-related tasks.