A procedure is described for reconstructing three-dimensional objects from two-dimensional projections. The method is based both on the original Crowther, DeRosier, and Klug (DeRosier, D.J., and Klug, A. (1968), Nature 217, 130-134; Crowther, R.A., DeRosier, D.J., and Klug, A. (1970) Proc. R. Soc. London A 317, 319-340) work on image reconstructions of icosahedral viruses and on the concept of noncrystallographic symmetry (Rossmann, M.G., 1995, Curr. Opin. Struct. Biol. 5, 650-655). The procedure has been applied so far only to test data where the objective has been the determination of particle orientation, both ab initio and through the use of model data. 1999 Academic Press.