Symmetry provides a source of redundancy which can be exploited in image reconstruction. In particular, internal
symmetries in molecules can help to compensate for the loss of Fourier phase information in macromolecular x-ray
crystallography. Symmetry projections are incorporated into iterative projection algorithms for reconstruction
of macromolecular electron densities from x-ray diffraction amplitudes from crystals. The effects of interpolation
are studied and the algorithms are applied to reconstruction of an icosahedral virus.