Electronic phase diagram of LixCoO2 has been re-examined using potentiostatically deintercalated single crystal samples. Stable phases of x ∼ 0.87, 0.72, 0.53, 0.50, 0.43, and 0.33 were found and isolated for physical property studies. A-type and chain-type antiferromagnetic orderings have been suggested from magnetic susceptibility measurement results in x ∼ 0.87 and 0.50 below ∼ 10K and 200K, respectively, similar to those found in NaxCoO2 system. There is no Li vacancy superlattice ordering observed at room temperature for the electronically stable phase Li0.72CoO2 as revealed by synchrotron X-ray Laue diffraction. The peculiar magnetic anomaly near ∼175K as often found in powder samples of x∼0.46-0.78 cannot be isolated through this single crystal potentiostatic method, which supports the previously proposed explanation to be surface stabilized phase of significant thermal hysteresis and aging character.