The problem of reconstructing an isolated particle from its projections, using spherical harmonics to represent the scattering density, is reformulated. A technique that makes explicit and efficient use of the symmetry to describe the angular part of the scattering density is developed in full detail for the particular case of icosahedral symmetry. It provides a very concise method, where the effort is concentrated in the determination of the radial part of the Fourier transform of the particle scattering density. The method allows individual-image model-independent view determination. An illustrative numerical example is given. (C) 2003 Elsevier Inc. All rights reserved.