This study develops a new gauge condition for performing long duration numerical evolutions of Einstein’’s equation on cosmological spacetimes with non-trivial spatial topologies. This new gauge makes it possible to perform reliable numerical evolutions on these manifolds in which the spatial volumes become more than one million times larger. This new condition was tested for this study by evolving homogeneous and isotropic initial data on exemplar manifolds with three spatial topologies: Sixth-Turn space, the lens space L(5, 2), and the Seifert fiber space SFS[S2 : (2, 1)(2, 1)(2, -1)].