  We present a discrete form of the Wheeler-DeWitt equation for quantum
gravitation, based on the lattice formulation due to Regge. In this setup the
infinite-dimensional manifold of 3-geometries is replaced by a space of
three-dimensional piecewise linear spaces, with the solutions to the lattice
equations providing a suitable approximation to the continuum wave functional.
The equations incorporate a set of constraints on the quantum wavefunctional,
arising from the triangle inequalities and their higher dimensional analogs.
The character of the solutions is discussed in the strong coupling (large $G$)
limit, where it is shown that the wavefunctional only depends on geometric
quantities, such as areas and volumes. An explicit form, determined from the
discrete wave equation supplemented by suitable regularity conditions, shows
peaks corresponding to integer multiples of a fundamental unit of volume. An
application of the variational method using correlated product wavefunctions
suggests a relationship between quantum gravity in $n+1$ dimensions, and
averages computed in the Euclidean path integral formulation in $n$ dimensions.
The proposed discrete equations could provide a useful, and complementary,
computational alternative to the Euclidean lattice path integral approach to
quantum gravity.
