The vibrational spectroscopy of the electronically closed-shell (Al2O3)(n)(AlO)(+) cations with n = 1-4 is studied in the 530-1200 cm(-1) range by infrared predissociation spectroscopy of the corresponding ion-He atom complexes in combination with quantum chemical calculations. In all cases we find, assisted by a genetic algorithm, global minimum structures that differ considerably from those derived from known modifications of bulk alumina. The n = 1 and n = 4 clusters exhibit an exceptionally stable conical structure of C-3v symmetry, whereas for n = 2 and n = 3, multiple isomers of lower symmetry and similar energy may contribute to the recorded spectra. A blue shift of the highest energy absorption band is observed with increasing cluster size and attributed to a shortening of Al-O bonds in the larger clusters. This intense band is assigned to vibrational modes localized on the rim of the conical structures for n = 1 and n = 4 and may aid in identifying similar, highly symmetric structures in larger ions.