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 simplices defined by the same set of vertices. I demonstrate, using numerical simulations, that allowing for this type of degeneracy substantially reduces the geometric finite-size effects, especially in the crumpled phase of the model; in other respects the phase structure of the model is not affected.