This study presents solid-state NMR measurements on β-amyloid (Aβ1-40) fibrils, providing experimental constraints on their quaternary structure. The data reveal internal and external quaternary contacts between β-sheets in the fibrils. Internal contacts occur within a single molecular layer, while external contacts occur between layers. Key findings include crosspeaks in 13C-13C and 15N-13C NMR spectra indicating specific sidechain interactions, such as between L17 and F19, I32, L34, and V36, and between I31 and G37. Additionally, salt bridge interactions between D23 and K28 sidechains are detected. Isotopic dilution experiments help distinguish intramolecular and intermolecular contacts. Based on these data and previous structural constraints, molecular models of Aβ1-40 fibrils are constructed using restrained molecular dynamics simulations and energy minimization. These models suggest a cross-β structure with internal and external quaternary contacts, consistent with experimental data. The study also shows that Aβ1-40 fibrils grown under different conditions can have different internal quaternary contacts. The results support a C2z quaternary structure with specific sidechain conformations. The models are consistent with electron microscopy and NMR data, and the study highlights the structural polymorphism of Aβ1-40 fibrils. The findings contribute to understanding the structural basis of amyloid fibrils and their role in diseases like Alzheimer's.This study presents solid-state NMR measurements on β-amyloid (Aβ1-40) fibrils, providing experimental constraints on their quaternary structure. The data reveal internal and external quaternary contacts between β-sheets in the fibrils. Internal contacts occur within a single molecular layer, while external contacts occur between layers. Key findings include crosspeaks in 13C-13C and 15N-13C NMR spectra indicating specific sidechain interactions, such as between L17 and F19, I32, L34, and V36, and between I31 and G37. Additionally, salt bridge interactions between D23 and K28 sidechains are detected. Isotopic dilution experiments help distinguish intramolecular and intermolecular contacts. Based on these data and previous structural constraints, molecular models of Aβ1-40 fibrils are constructed using restrained molecular dynamics simulations and energy minimization. These models suggest a cross-β structure with internal and external quaternary contacts, consistent with experimental data. The study also shows that Aβ1-40 fibrils grown under different conditions can have different internal quaternary contacts. The results support a C2z quaternary structure with specific sidechain conformations. The models are consistent with electron microscopy and NMR data, and the study highlights the structural polymorphism of Aβ1-40 fibrils. The findings contribute to understanding the structural basis of amyloid fibrils and their role in diseases like Alzheimer's.