The functional architecture of human cortex can be modeled as high-dimensional representational spaces in which patterns of brain activity are recast as vectors with basis functions that have tuning profiles and patterns of connectivity that are common across brains. Transformation matrices that rotate individual anatomical spaces into the common model space are derived with searchlight-based, whole cortex hyperalignment. Patterns of brain activity in individual brains are modeled as multiplexed topographic basis functions. This model provides a common structure that captures finegrained distinctions among cortical patterns of response that are not modeled well by current brain atlases.