  The three-body $KK\bar K$ model for the $K(1460)$ resonance is developed on
the basis of the Faddeev equations in configuration space. A single-channel
approach is using with taking into account the difference of masses of neutral
and charged kaons. It is demonstrated that a splitting the mass of the
$K(1460)$ resonance takes a place around 1460 MeV according to $K^0K^0{\bar
K}^0$, $K^0K^+K^-$ and $K^+K^0{\bar K}^0$, $ K^+K^+K^-$ neutral and charged
particle configurations, respectively. The calculations are performed with two
sets of $KK$ and $K\bar K$ phenomenological potentials, where the latter
interaction is considered the same for the isospin singlet and triplet states.
The effect of repulsion of the $KK$ interaction on the mass of the $KK\bar K$
system is studied and the effect of the mass polarization is evaluated. The
first time the Coulomb interaction for description of the $K(1460)$ resonance
is considered. The mass splitting in the $K$(1460) resonances is evaluated to
be in range of 10 MeV with taking into account the Coulomb force. The
three-body model with the $K\bar K$ potential, which has the different strength
of the isospin singlet and triplet parts that are related by the condition of
obtaining a quasi-bound three-body state is also considered. Our results are in
reasonable agreement with the experimental mass of the $K(1460)$ resonance.
