A genetic algorithm-based computational method for the ab initio phasing of diffraction data from crystals of symmetric macromolecular structures, such as icosahedral viruses, has been implemented and applied to authentic data from the P1/Mahoney strain of poliovirus. Using only single-wavelength native diffraction data, the method is shown to be able to generate correct phases, and thus electron density, to 3.0 A resolution. Beginning with no advance knowledge of the shape of the virus and only approximate knowledge of its size, the method uses a genetic algorithm to determine coarse, low-resolution (here, 20.5 A) models of the virus that obey the known non-crystallographic symmetry (NCS) constraints. The best scoring of these models are subjected to refinement and NCS-averaging, with subsequent phase extension to high resolution (3.0 A). Initial difficulties in phase extension were overcome by measuring and including all low-resolution terms in the transform. With the low-resolution data included, the method was successful in generating essentially correct phases and electron density to 6.0 A in every one of ten trials from different models identified by the genetic algorithm. Retrospective analysis revealed that these correct high-resolution solutions converged from a range of significantly different low-resolution phase sets (average differences of 59.7 degrees below 24 A). This method represents an efficient way to determine phases for icosahedral viruses, and has the advantage of producing phases free from model bias. It is expected that the method can be extended to other protein systems with high NCS.