As the primary toxic species in the etiology of Alzheimer disease (AD) are low molecular weight oligomers of Aβ, it is crucial to understand the structure of Aβ oligomers for gaining molecular insights into AD pathology. We have earlier demonstrated that in the presence of fatty acids, Aβ42 peptides assemble as 12-24mer oligomers. These Large Fatty Acid-derived Oligomers (LFAOs) exist predominantly as 12mers at low and as 24mers at high concentrations. The 12mers are more neurotoxic than the 24mers and undergo self-replication, while the latter propagate to morphologically distinct fibrils with succinct pathological consequences. In order to glean into their functional differences and similarities, we have determined their structures in greater detail by combining molecular dynamic simulations with biophysical measurements. We conjecture that the LFAO are made of Aβ units in an S-shaped conformation, with the 12mers forming a double-layered hexamer ring (6 × 2) while the structure of 24mers is a double-layered dodecamer ring (12 × 2). A closer inspection of the (6 × 2) and (12 × 2) structures reveals a concentration and pH dependent molecular reorganization in the assembly of 12 to 24mers, which seems to be the underlying mechanism for the observed biophysical and cellular properties of LFAOs.