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Abstract Current brain mapping methods highly depend on the regularity, or commonality, of anatomical structure, by forcing the same atlas to be matched to different brains. As a result, individualized structural information can be overlooked. Recently, we conceptualized a new type of cortical folding pattern called the 3-hinge gyrus (3HG), which is defined as the conjunction of gyri coming from three directions. Many studies have confirmed that 3HGs are not only widely existing on different brains, but also possess both common and individual patterns. In this work, we put further effort, based on the identified 3HGs, to establish the correspondences of individual 3HGs. We developed a learning-based embedding framework to encode individual cortical folding patterns into a group of anatomically meaningful embedding vectors (cortex2vector). Each 3HG can be represented as a combination of these embedding vectors via a set of individual specific combining coefficients. In this way, the regularity of folding pattern is encoded into the embedding vectors, while the individual variations are preserved by the multi-hop combination coefficients. Results show that the learned embeddings can simultaneously encode the commonality and individuality of cortical folding patterns, as well as robustly infer the complicated many-to-many anatomical correspondences among different brains.