Amyloidogenic model peptides are invaluable for investigating assembly mechanisms in disease related amyloids and in protein folding. During aggregation, such peptides can undergo bifurcation leading to fibrils or crystals, however the mechanisms of fibril-to-crystal conversion are unclear. We navigate herein the energy landscape of amyloidogenic peptides by studying a homologous series of hexapeptides found in animal, human and disease related proteins. We observe fibril-to-crystal conversion occurring within single aggregates via untwisting of twisted ribbon fibrils possessing saddle-like curvature and cross-sectional aspect ratios approaching unity. Changing sequence, pH or concentration shifts the growth towards larger aspect ratio species assembling into stable helical ribbons possessing mean-curvature. By comparing atomistic calculations of desolvation energies for association of peptides we parameterise a kinetic model, providing a physical explanation of fibril-to-crystal interconversion. These results shed light on the self-assembly of amyloidogenic peptides, suggesting amyloid crystals, not fibrils, represent the ground state of the protein folding energy landscape.