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$\ensuremath{\gamma}$-alumina is usually described as a defect spinel structure with cation site vacancies distributed randomly between octahedral and tetrahedral positions. Its structure and properties are still not well understood. Using ab initio calculations based on density functional theory and plane-wave pseudopotentials, we investigate all possible vacancy configurations within a 40-atom unit cell, which are consistent with the crystallographic data available. We find that the minimum energy structure has all the vacancies located at octahedral sites. Results are presented for the atomic configuration, bulk modulus, and electronic density of states of this structure.

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