Our society's environmental and economic progress depends on the development of high-performance materials such as lightweight alloys, high-energy-density battery materials, recyclable motor vehicle and building components, and energy-efficient lighting. Meeting these needs requires us to understand the central role of crystal structure in a material's properties. Despite more than 50 years of progress in first-principles calculations, it is still impossible in most materials to infer ground-state properties purely from a knowledge of their atomic components-a situation described as 'scandalous' in the well-known essay by Maddox(1). Many methods attempt to predict crystal structures and compound stability, but here I take a different tack-to infer the existence of structures on the basis of combinatorics and geometric simplicity(2). The method identifies 'least random' structures, for which the energy is an extremum ( maximum or minimum). Although the key to the generic nature of the approach is energy minimization, the extrema are found in a chemistry-independent way.