Aggregated tau protein is associated with over 20 neurological disorders, which include Alzheimer's disease. Previous work has shown that tau's sequence segments VQIINK and VQIVYK drive its aggregation, but inhibitors based on the structure of the VQIVYK segment only partially inhibit full-length tau aggregation and are ineffective at inhibiting seeding by full-length fibrils. Here we show that the VQIINK segment is the more powerful driver of tau aggregation. Two structures of this segment determined by the cryo-electron microscopy method micro-electron diffraction explain its dominant influence on tau aggregation. Of practical significance, the structures lead to the design of inhibitors that not only inhibit tau aggregation but also inhibit the ability of exogenous full-length tau fibrils to seed intracellular tau in HEK293 biosensor cells into amyloid. We also raise the possibility that the two VQIINK structures represent amyloid polymorphs of tau that may account for a subset of prion-like strains of tau.