  A significant fraction of extended radio sources presents a peculiar X-shaped
radio morphology: in addition to the classical double lobed structure, radio
emission is also observed along a second axis of simmetry in the form of
diffuse wings or tails. In a previous investigation we showed the existence of
a connection between the radio morphology and the properties of the host
galaxies. Motivated by this connection we performed two-dimensional numerical
simulations showing that X-shaped radio sources may naturally form as a jet
propagates along the major axis a highly elliptical density distribution,
because of the fast expansion of the cocoon along the minor axis of the
distribution.
  We intend to extend our analysis by performing three-dimensional numerical
simulations and investigating the role of different parameters is determining
the formation of the X-shaped morphology.
  The problem is addressed by numerical means, carrying out three-dimensional
relativistic magnetohydrodynamic simulations of bidirectional jets propagating
in a triaxial density distribution.
  We show that only jets with power $\lesssim 10^{44}$ erg s$^{-1}$ can give
origin to an X-shaped morphology and that a misalignment of $30^o$ between the
jet axis and the major axis of the density distribution is still favourable to
the formation of this kind of morphology. In addition we compute synthetic
radio emission maps and polarization maps.
  In our scenario for the formation of X-shaped radio sources only low power
FRII can give origin to such kind of morphology. Our synthetic emission maps
show that the different observed morphologies of X-shaped sources can be the
result of similar structures viewed under different perspectives.
