  A family of exact relativistic stellar models is described. The family
generalizes Buchdahl's n=1 polytropic solution. The matter content is a perfect
fluid and, excluding Buchdahl's original model, it behaves as a liquid at low
pressures in the sense that the energy density is non-zero in the zero pressure
limit. The equation of state has two free parameters, a scaling and a stiffness
parameter. Depending on the value of the stiffness parameter the fluid
behaviour can be divided in four different types. Physical quantities such as
masses, radii and surface redshifts as well as density and pressure profiles
are calculated and displayed graphically. Leaving the details to a later
publication, it is noted that one of the equation of state types can quite
accurately approximate the equation of state of real cold matter in the outer
regions of neutron stars. Finally, it is observed that the given equation of
state does not admit models with a conical singularity at the center.
