We consider discretized gravity in six dimensions, where the two extra dimensions have been compactified on a hyperbolic disk of constant curvature. We analyze different realizations of lattice gravity on the disk at the level of an effective field theory for massive gravitons. It is shown that the observed strong coupling scale of lattice gravity in discretized five-dimensional flat or warped space can be increased when the latticized fifth dimension is wrapped around a hyperbolic disk that

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... a non-trivial warp factor. As an application, we also discuss the generation of naturally small Dirac neutrino masses via a discrete volume suppression mechanism and discuss briefly collider implications of our model.