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We revisit the calculation of the three-loop diagrams for the radiative neutrino mass generation and consider some relevant constraints on the model recently proposed by Jin et al. (2015) [1]. We find that the previous approximation is inappropriate due to the neglect of some important contributions, and the benchmark point proposed can neither give rise to enough neutrino masses nor accommodate these additional constraints, such as the validity of the perturbation theory, the electroweak precision measurements, and the neutrinoless double beta decays.