The crystal structures of the gamma, beta, and alpha'(H) forms of dicalcium silicate (C2S) have been refined by Rietveld analysis of synchrotron X-ray data. The powder refinement of gamma-C2S, Bragg R = 4.01%, is of comparable quality to the reported single crystal refinement. The refinement of beta-C2S (stabilized with 0.5 wt % Cr2O3) gives a Bragg R of 3.84% and confirms the latest single crystal refinement obtained from twinned data. The alpha'(H)-C2S polymorph is produced when C2S is stabilized with 5 moi % Ca-3(PO4)(2), C3P; for this phase, a disordered structure with all atoms except Si split into two half-occupied mirror-related positions refined to give a Bragg R of 3.58%. The structure of ''alpha-C2S'', prepared by stabilizing C2S with 10 mol% C3P, corresponds to 6Ca(2)SiO(4) . 1Ca(3)(PO4)(2). Rietveld refinement using synchrotron X-ray powder data gives a Bragg R of 6.4% and confirms the single crystal structure which, due to twinning, was previously determined using superlattice reflections only. A structure for stoichiometric alpha-C2S is proposed, based on the high temperature form of K2SO4. Powder diffraction patterns calculated from the crystal structure parameters are presented in graphical and numerical form for the C2S phases and related compounds. These patterns are free from the usual experimental uncertainties present in observed patterns and thus may be used to facilitate the identification and quantification of these closely-related and complex phases in mixtures.