The electronic and geometrical structures of the clusters composed of 12 iron and 12 oxygen atoms are obtained using all-electron density functional theory. It is found that the states with geometrical structures corresponding to oxygen chemisorbed on the ground-state Fe-12 cluster surface (Fe12O12) are close in total energy to the states whose geometrical configurations are hollow cages (FeO)(12). The lowest total energy state is the ferrimagnetic triplet state of Fe12O12. A ferrimagnetic nonet state of (FeO)(12) is only marginally higher in total energy. The clusters are rich in nearly degenerate isomers. Oxygen adsorption dramatically quenches the spin of Fe-12 clusters. (C) 2012 Elsevier B. V. All rights reserved.