Polyglutamine expansion within the exon1 of huntingtin leads to protein misfolding, aggregation, and cytotoxicity in Huntington's disease. This incurable neurodegenerative disease is the most prevalent member of a family of CAG repeat expansion disorders. Although mature exon1 fibrils are viable candidates for the toxic species, their molecular structure and how they form have remained poorly understood. Using advanced magic angle spinning solid-state NMR, we directly probe the structure of the rigid core that is at the heart of huntingtin exon1 fibrils and other polyglutamine aggregates, via measurements of long-range intramolecular and intermolecular contacts, backbone and side-chain torsion angles, relaxation measurements, and calculations of chemical shifts. These experiments reveal the presence of β-hairpin-containing β-sheets that are connected through interdigitating extended side chains. Despite dramatic differences in aggregation behavior, huntingtin exon1 fibrils and other polyglutamine-based aggregates contain identical β-strand-based cores. Prior structural models, derived from X-ray fiber diffraction and computational analyses, are shown to be inconsistent with the solid-state NMR results. Internally, the polyglutamine amyloid fibrils are coassembled from differently structured monomers, which we describe as a type of "intrinsic" polymorphism. A stochastic polyglutamine-specific aggregation mechanism is introduced to explain this phenomenon. We show that the aggregation of mutant huntingtin exon1 proceeds via an intramolecular collapse of the expanded polyglutamine domain and discuss the implications of this observation for our understanding of its misfolding and aggregation mechanisms.