  Given a trivalent graph in the 3-dimensional Euclidean space, we call it a
discrete surface because it has a tangent space at each vertex determined by
its neighbor vertices. To abstract a continuum object hidden in the discrete
surface, we introduce a subdivision method by applying the Goldberg-Coxeter
subdivision and discuss the convergence of a sequence of discrete surfaces
defined inductively by the subdivision. We also study the limit set as the
continuum geometric object associated with the given discrete surface.
