The Symmetry and Topology of Finite and Periodic Graphs and Their Embeddings in Three-Dimensional Euclidean Space

Michael O’keeffe, Michael M.J. Treacy

Research output: Contribution to journalArticlepeer-review

Abstract

We make the case for the universal use of the Hermann-Mauguin (international) notation for the description of rigid-body symmetries in Euclidean space. We emphasize the importance of distinguishing between graphs and their embeddings and provide examples of 0-, 1-, 2-, and 3-periodic structures. Embeddings of graphs are given as piecewise linear with finite, non-intersecting edges. We call attention to problems of conflicting terminology when disciplines such as materials chemistry and mathematics collide.

Original languageEnglish (US)
Article number822
JournalSymmetry
Volume14
Issue number4
DOIs
StatePublished - Apr 2022

Keywords

  • graphs
  • Hermann–Mauguin notation
  • knots
  • links
  • nets
  • tangles

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

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