  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 has 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.
