Three-Dimensional Simplicial Gravity and Degenerate Triangulations

I define a model of three-dimensional simplicial gravity using an extended ensemble of triangulations where, in addition to the usual combinatorial triangulations, I allow degenerate triangulations, i.e. triangulations with distinct simplexes defined by the same set of vertexes. I demonstrate, using numerical simulations, that allowing this type of degeneracy substantially reduces the geometric finite-size effects, especially in the crumpled phase of the model, in other respect the phase structure of the model is not affected.