The human ventral visual stream has a highly systematic organization of object information, but the causal pressures driving these topographic motifs are highly debated. Here, we use self-organizing principles to learn a topographic representation of the data manifold of a deep neural network representational space. We find that a smooth mapping of this representational space showed many brain-like motifs, with a large-scale organization by animacy and real-world object size, supported by mid-level feature tuning, with naturally emerging face- and scene-selective regions. While some theories of the object-selective cortex posit that these differently tuned regions of the brain reflect a collection of distinctly specified functional modules, the present work provides computational support for an alternate hypothesis that the tuning and topography of the object-selective cortex reflect a smooth mapping of a unified representational space.