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Even basic questions of how limb pose is represented in the somatosensory cortex are unclear. We developed a topographic variational autoencoder with lateral connectivity (topo-VAE) to compute a putative cortical map from a large set of natural movement data. Although not fitted to neural data, our model reproduces two sets of observations from monkey centre-out reaching: 1. The shape and velocity dependence of proprioceptive receptive fields in hand-centered coordinates despite the model having no knowledge of arm kinematics or hand coordinate systems. 2. The distribution of neuronal preferred directions (PDs) recorded from multi-electrode arrays. The model makes several testable predictions: 1. Encoding across the cortex has a blob-and-pinwheel-type geometry of PDs. 2. Few neurons will encode just a single joint. 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