Peptide foldamers constitute a growing class of nanomaterials with potential applications in a wide variety of chemical, medical and technological fields. Here we describe the preparation and structural characteristics of a new class of cyclic peptide foldamers (3alpha,gamma-CPs) that, depending on their backbone N-methylation patterns and the medium, can either remain as flat rings that dimerize through arrays of hydrogen bonds of antiparallel beta-sheet type, or can fold into twisted double reverse turns that, in the case of double gamma-turns, associate in nonpolar solvents to form helical supramolecular structures. A 3alpha,gamma-CP consists of a number of multiples of a repeat unit made up of four amino acid residues of alternating chirality: three corresponding to alpha-amino acids and one to a gamma-amino acid (a cis-3-aminocycloalkanecarboxylic acid).