  We study a realization of the topology of the Zee model for the generation of
neutrino masses at one-loop with a minimal set of vector-like fermions. After
imposing an exact $Z_2$ symmetry to avoid tree-level Higgs-mediated flavor
changing neutral currents, one dark matter candidate is obtained from the
subjacent inert doublet model, but with the presence of new co-annihilating
particles. We show that the model is consistent with the constraints coming
from lepton flavor violation processes, oblique parameters, dark matter and
neutrino oscillation data.
