This study investigates the quaternary structure of Alzheimer's β-amyloid (Aβ1-40) fibrils using solid-state nuclear magnetic resonance (NMR) spectroscopy. The authors identify internal and external quaternary contacts between β-sheet segments within and between molecular layers, respectively. Internal contacts are observed between sidechains of L17 and F19, I32, L34, and V36, while external contacts are found between I31 and G37, and M35 and G33. Salt bridge interactions between D23 and K28 are also detected. Isotopic dilution experiments help distinguish intramolecular from intermolecular contacts. The findings are used to construct molecular models of Aβ1-40 fibrils, which show that the quaternary structure is dictated by a set of contacts among amino acid sidechains projecting from adjacent β-sheets. The models suggest that the quaternary structure is polymorphic, with different internal quaternary contacts observed in fibrils grown under agitation versus quiescence. The study also discusses the implications of these findings for the alignment of internal quaternary contacts and the resemblance of amyloid fibril structures to those of β-helical proteins.This study investigates the quaternary structure of Alzheimer's β-amyloid (Aβ1-40) fibrils using solid-state nuclear magnetic resonance (NMR) spectroscopy. The authors identify internal and external quaternary contacts between β-sheet segments within and between molecular layers, respectively. Internal contacts are observed between sidechains of L17 and F19, I32, L34, and V36, while external contacts are found between I31 and G37, and M35 and G33. Salt bridge interactions between D23 and K28 are also detected. Isotopic dilution experiments help distinguish intramolecular from intermolecular contacts. The findings are used to construct molecular models of Aβ1-40 fibrils, which show that the quaternary structure is dictated by a set of contacts among amino acid sidechains projecting from adjacent β-sheets. The models suggest that the quaternary structure is polymorphic, with different internal quaternary contacts observed in fibrils grown under agitation versus quiescence. The study also discusses the implications of these findings for the alignment of internal quaternary contacts and the resemblance of amyloid fibril structures to those of β-helical proteins.