  We derive the Lie point symmetries for the MIT Bag Model for quark stars in
relativistic astrophysics. Four cases of reduction arise; three cases of
specific values of the measure of the anisotropy variation, and one general
case, which we postulate as a specific relationship between the two
gravitational potentials. We demonstrate the applicability of the model by
generating two closed form solutions that satisfy the master gravitational
equation and we match the interior geometries of the gravitating hyperspheres
with the external solution given by the Reissner-Nordstr\"{o}m metric at the
stellar boundary. Lastly, we produce a general class of solutions that are
attainable for smooth and continuous functions and generate two exact solutions
using this model.
