Phase Retrieval for Icosahedral Particles

X-ray crystallography is a technique for determining the structures of molecules [1,2]. It involves irradiating a crystalline specimen of the molecule with a monochromatic beam of x-rays and measuring the resulting diffraction pattern. The complex amplitude of the diffracted x-rays is equal to the Fourier transform of the electron density in the crystalline specimen, and only the intensity, but not the phase, of the diffracted x-rays can be measured. Reconstruction of the electron density therefore constitutes a phase problem.