Construction of continuum from a discrete surface by its iterated subdivisions

Motoko Kotani, Hisashi Naito, Chen Tao

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Jun 9

ASJC Scopus subject areas

  • General

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