Alzheimer's, Parkinson's, and Creutzfeldt-Jakob's neurodegenerative diseases are all linked with the assembly of normally soluble proteins into amyloid fibrils. Because of experimental limitations, structural characterization of the soluble oligomers, which form early in the process of fibrillogenesis and are cytotoxic, remains to be determined. In this article, we study the aggregation paths of seven chains of the shortest amyloid-forming peptide, using an activitated method and a reduced atomic representation. Our simulations show that disordered KFFE monomers ultimately form three distinct topologies of similar energy: amorphous oligomers, incomplete rings with beta-barrel character, and cross-beta-sheet structures with the meridional but not the equatorial X-ray fiber reflections. The simulations also shed light on the pathways from misfolded aggregates to fibrillar-like structures. They also underline the multiplicity of building blocks that can lead to the formation of the critical nucleus from which rapid growth of the fibril occurs.