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 sub-division 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 objects associated with the given discrete surface.
|Publication status||Published - 2018 Jun 9|
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