The 15 ground-state core structures that emerge from all of the 11,440 HP sequences of the type described in Fig. 1. Only H residues and H—H string bonds are shown. The pair of numbers at the lower right of each structure are (respectively) the number of sequential H-segments and the number of H—H string bonds contained in the sequence folding to the structure. The symmetry of the core is abbreviated by the terms ν0 ν1, ν1/2, and FRUST (i.e., frustrated). The ground-state core geometry of any sequence is uniquely determined by set of internally clamped sequential H-segments along its length (e.g., the geometry ν0 3 3 corresponds to all permutations of the four fragments (H—H … H—H … H—H … H). The number of sequences folding to a particular geometry is given by the total number of permutations, which do not break, create, or extend the length of the sequential H-segments.