  We investigate quantum gravity in four dimensions using the Regge approach on
triangulations of the four-torus with general, non-regular incidence matrices.
We find that the simplicial lattice tends to develop spikes for vertices with
low coordination numbers even for vanishing gravitational coupling. Different
to the regular, hypercubic lattices almost exclusively used in previous
studies, we find now that the observables depend on the measure. Computations
with nonvanishing gravitational coupling still reveal the existence of a region
with well-defined expectation values. However, the phase structure depends on
the triangulation. Even with additional higher- order terms in the action the
critical behavior of the system changes with varying (local) coordination
numbers.
