  We extend a model of four-dimensional simplicial quantum gravity to include
degenerate triangulations in addition to combinatorial triangulations
traditionally used. Relaxing the constraint that every 4-simplex is uniquely
defined by a set of five distinct vertexes, we allow triangulations containing
multiply connected simplexes and distinct simplexes defined by the same set of
vertexes. We demonstrate numerically that including degenerated triangulations
substantially reduces the finite-size effects in the model. In particular, we
provide a strong numerical evidence for an exponential bound on the entropic
growth of the ensemble of degenerate triangulations, and show that a
discontinuous crumpling transition is already observed on triangulations of
volume N_4 ~= 4000.
