Studies of peptide-based nanostructures provide general insights into biomolecular self-assembly and can lead material engineering toward technological applications. The diphenylalanine peptide (FF) self-assembles into discrete, hollow, well ordered nanotubes, and its derivatives form nanoassemblies of various morphologies. Here we demonstrate for the first time, to our knowledge, the formation of planar nanostructures with beta-sheet content by the triphenylalanine peptide (FFF). We characterize these structures using various microscopy and spectroscopy techniques. We also obtain insights into the interactions and structural properties of the FF and FFF nanostructures by 0.4-micros, implicit-solvent, replica-exchange, molecular-dynamics simulations of aqueous FF and FFF solutions. In the simulations the peptides form aggregates, which often contain open or ring-like peptide networks, as well as elementary and network-containing structures with beta-sheet characteristics. The networks are stabilized by polar and nonpolar interactions, and by the surrounding aggregate. In particular, the charged termini of neighbor peptides are involved in hydrogen-bonding interactions and their aromatic side chains form "T-shaped" contacts, as in three-dimensional FF crystals. These interactions may assist the FF and FFF self-assembly at the early stage, and may also stabilize the mature nanostructures. The FFF peptides have higher network propensities and increased aggregate stabilities with respect to FF, which can be interpreted energetically.