  This paper examines the behaviour of closed `lattice universes' wherein
masses are distributed in a regular lattice on the Cauchy surfaces of closed
vacuum universes. Such universes are approximated using a form of Regge
calculus originally developed by Collins and Williams to model closed FLRW
universes. We consider two types of lattice universes, one where all masses are
identical to each other and another where one mass gets perturbed in magnitude.
In the unperturbed universe, we consider the possible arrangements of the
masses in the Regge Cauchy surfaces and demonstrate that the model will only be
stable if each mass lies within some spherical region of convergence. We also
briefly discuss the existence of Regge models that are dual to the ones we have
considered. We then model a perturbed lattice universe and demonstrate that the
model's evolution is well-behaved, with the expansion increasing in magnitude
as the perturbation is increased.
