Abstract
A density-functional theory is developed to calculate the elastic moduli of crystals and quasicrystals. It is found that the nonaffine character of deformations below the unit-cell scale causes the Poisson ratio of a hard-sphere solid to be negative. An elastic instability is found for the icosahedral quasicrystals which lowers their symmetry to ${D}_{3}$ or ${D}_{5}$. The distortions of the diffraction pattern are in qualitative agreement with experiments.
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