We investigate structural properties of large vacancy agglomerates in Si and GaAs using a self-consistent-charge density-functional based tight-binding method. We also calculated the defect-related positron lifetimes. Strong evidence is found for the existence of vacancy aggregates with unusual magic numbers in GaAs. In contrast to Si - the first stable agglomerate consists 12 vacancies instead of 6. This findings fit into experimental observations on deformed and irradiated samples.