  Buchdahl sphere, the limiting stable isotropic stellar structure without
exotic matter, plays a very important role in our understanding of how compact
an astrophysical object can be. Here, we show certain universal properties
associated with the Buchdahl sphere, in the sense that these properties will
not change with the inclusion of electric charge in the stellar structure, or,
will hold good in the pure Lovelock theories of gravity as well. Using these
universalities, we have proposed a Buchdahl limit for a slowly-rotating stellar
configuration, for the first time. Finally, the universality of the Buchdahl
sphere in terms of the gravitational and non-gravitational field energies, as
well as for the photon sphere have also been discussed.
