  Deformation theory for 2-dimensional dynamical triangulations with N vertices
is discussed by exploiting the geometry of the moduli space of Euclidean
polygons. Such an analysis provides an explicit connection among Regge
surfaces, dynamical triangulations and the Witten-Kontsevich model. We show
that a natural set of Regge measures and a triangulation counting of relevance
for dynamical triangulations are directly connected with intersection theory
over the compactified moduli space of genus g Riemann surfaces with N
punctures.The Regge measures in question provide volumes of the open strata in
moduli space. It is also argued that the arguments presented here offer
evidence of a form of topological S-duality between Regge calculus and DT
theory.
