In physics, standard cosmology is build with simple maximally symmetric 3-manifolds (spacelike time-slices of constant curvature, e.g. $S^3$ or less popular the hyperbolic space $H^3$). Since $S^3$ has a finite volume it seems natural to ask whether there also exists a maximally symmetric hyperbolic counterpart which also has a finite volume? (An answer in layman's terms would be fine, if possible.)