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In the framework of the Faddeev equations in configuration space, weinvestigate the $K$(1460) meson as a resonant state of the $KK\bar{K}$ kaonicsystem. 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 ofthe kaon mass difference and the attractive Coulomb force between the$K^{+}K^{-}$ pair. We found that the Coulomb shift adds over 1 MeV to thethree-body binding energy. The expected correction to the binding energy due tomass redistribution from $AA$ to $AB$ is found to be negligible, up to amaximum of 6\% of the relative mass correction. At the same time, the symmetryof the wave function is distorted depending on the mass ratio value. We foundthat the repulsive $KK$ interaction plays essential role in the binding energyof the $KK\bar K$ system and report the mass of 1461.8 or 1464.1 MeV for theneutral $K^{0}$(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.

The charge and mass symmetry breaking in the $KK\bar{K}$ system