(Z2)3 symmetry of the tripartite model

We derive in a simple way the (Z2)3 symmetry which characterizes uniquely the phenomenologically successful tripartite form leading to the tribimaximal mixing in the neutrino mass matrix. We impose this symmetry in a setup including the charged leptons and find that it can accommodate all the possible patterns of lepton masses in the framework of type-I and type-II seesaw mechanisms. We also discuss the possibility of generating enough baryon asymmetry through lepton-lepton asymmetry.