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We analytically and numerically characterize the structure of hard-spherefluids in order to review various geometrical frustration scenarios of theglass transition. We find generalized polytetrahedral order to be correlatedwith increasing fluid packing fraction, but to become increasingly irrelevantwith increasing dimension. We also find the growth in structural correlationsto be modest in the dynamical regime accessible to computer simulations.

Geometrical Frustration and Static Correlations in Hard-Sphere Glass Formers