Energetically favorable local interactions can overcome the entropic cost of chain ordering and cause otherwise flexible polymers to adopt regularly repeating backbone conformations. A prominent example is the α helix present in many protein structures, which is stabilized by i, i + 4 hydrogen bonds between backbone peptide units. With the increased chemical diversity offered by unnatural amino acids and backbones, it has been possible to identify regularly repeating structures not present in proteins, but to date, there has been no systematic approach for identifying new polymers likely to have such structures despite their considerable potential for molecular engineering. Here we describe a systematic approach to search through dipeptide combinations of 130 chemically diverse amino acids to identify those predicted to populate unique low-energy states. We characterize ten newly identified dipeptide repeating structures using circular dichroism spectroscopy and comparison with calculated spectra. NMR and X-ray crystallographic structures of two of these dipeptide-repeat polymers are similar to the computational models. Our approach is readily generalizable to identify low-energy repeating structures for a wide variety of polymers, and our ordered dipeptide repeats provide new building blocks for molecular engineering.