  The self-similar equilibrium models of self-gravitating, rotating, isothermal
systems are investigated analytically. In these models the rotation velocity is
constant and the density varies as $\frac{f(\theta, \phi)}{r^2}$, where $r$ and
$\theta$ are the spherical radius and the co-latitude, respectively. The
nonaxisymmetric solutions contain three free parameters, one of the parameters
depends on the rotation velocity. These parameters determine the overall shape
of the density distribution. By assuming that the dominant component of the
magnetic field is purely toroidal and the ratio of the purely toroidal magnetic
pressure to the gas pressure, $\alpha$, is spatially constant, the axisymmetric
solutions generalized so as the effect of magnetic field could be studied. We
find that the equilibria of axially symmetric systems yield ellipsoids or
spheres only when the ratio of rotation velocity to the sound speed is taken to
be $\sqrt{2\alpha}$.
