We report full quantum cross sections and rate constants for the O-18 + O-36(2) -> O-36(2) + O-18 collision process. This constitutes to the best of our knowledge the first dynamical study of the (OOO)-O-18-O-18-O-18 system, with three identical O-18 oxygen atoms. We emphasize the comparison with the O-16 + O-32(2) collision as this latter presents the exact same features as the one treated here, except the consistent change of mass for all three atoms. We find very similar behaviors in the cross sections, and we confirm that the rates are faster when three identical nuclei are involved. In particular, we cannot dynamically study this system with classical trajectory methods, and we have to include properly the indistinguishability of the three O-18 nuclei; however, we note some slight differences with the (OOO)-O-16-O-16-O-16 benchmark system, and we focus our analysis on their origin.