Variation in cortical connectivity profiles is typically modeled as having a coarse spatial scale parcellated into interconnected brain areas. We created a high-dimensional common model of the human connectome to search for fine-scale structure that is shared across brains. Projecting individual connectivity data into this new common model connectome accounts for substantially more variance in the human connectome than do previous models. This newly discovered shared structure is closely related to fine-scale distinctions in representations of information. These results reveal a shared fine-scale structure that is a major component of the human connectome that coexists with coarse-scale, areal structure. This shared fine-scale structure was not captured in previous models and was, therefore, inaccessible to analysis and study.