  Using a multi domain spectral method, we investigate systematically the
general-relativistic model for axisymmetric uniformly rotating, homogeneous
fluid bodies generalizing the analytically known Maclaurin and Schwarzschild
solutions. Apart from the curves associated with these solutions and a further
curve of configurations that rotate at the mass shedding limit, two more curves
are found to border the corresponding two parameter set of solutions. One of
them is a Newtonian lens shaped sequence bifurcating from the Maclaurin
spheroid sequence, while the other one corresponds to highly relativistic
bodies with an infinite central pressure. The properties of the configuration
for which both the gravitational and the baryonic masses, moreover angular
velocity, angular momentum as well as polar red shift obtain their maximal
values are discussed in detail. In particular, by comparison with the static
Schwarzschild solution, we obtain an increase of 34.25% in the gravitational
mass. Moreover, we provide exemplarily a discussion of angular velocity and
gravitational mass on the entire solution class.
