  In the framework of the Faddeev equations in configuration space, we
investigate the $K$(1460) meson as a resonant state of the $KK\bar{K}$ kaonic
system. We perform calculations for the particle configurations
$K^{0}K^{+}K^{-}$ and $K^{0}K^{+}\overline{{K}^{0}}$ within two models: the
$ABC $ model, in which all three particles are distinguishable, and the $AAC$
model when two particles are identical. The models differ in their treatment of
the kaon mass difference and the attractive Coulomb force between the
$K^{+}K^{-}$ pair. We found that the Coulomb shift adds over 1 MeV to the
three-body binding energy. The expected correction to the binding energy due to
mass redistribution from $AA$ to $AB$ is found to be negligible, up to a
maximum of 6\% of the relative mass correction. At the same time, the symmetry
of the wave function is distorted depending on the mass ratio value. We found
that the repulsive $KK$ interaction plays essential role in the binding energy
of the $KK\bar K$ system and report the mass of 1461.8 or 1464.1 MeV for the
neutral $K^{0}$(1460) and 1466.5 or 1468.8 MeV for the charged $K^{+}$(1460)
resonances, respectively, depending on the parameter sets for $KK$ and
$K\bar{K}$ interactions.
