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The atomic structure of the polar ZnO(0001) surfaces in a dry and humid oxygen environment is studied combining diffraction experiments and density-functional theory. Our results indicate that for similar stoichiometries a large number of very different, but energetically almost degenerate reconstructions exist. Thus vibrational entropy, which could be safely neglected for most semiconductor surfaces becomes dominant, giving rise to a hitherto not reported strong dependence of surface phase diagrams on temperature. Based on this insight we are able to consistently describe and explain the experimentally observed surface structures on polar ZnO(0001) surfaces.