Isogonal weavings on the sphere: Knots, links, polycatenanes

Michael O'Keeffe, Michael M.J. Treacy

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Mathematical knots and links are described as piecewise linear - straight, non-intersecting sticks meeting at corners. Isogonal structures have all corners related by symmetry ('vertex'-transitive). Corner- and stick-transitive structures are termed regular. No regular knots are found. Regular links are cubic or icosahedral and a complete account of these (36 in number) is given, including optimal (thickest-stick) embeddings. Stick 2-transitive isogonal structures are again cubic and icosahedral and also encompass the infinite family of torus knots and links. The major types of these structures are identified and reported with optimal embeddings. The relevance of this work to materials chemistry and biochemistry is noted.

Original languageEnglish (US)
Pages (from-to)611-621
Number of pages11
JournalActa Crystallographica Section A: Foundations and Advances
StatePublished - Sep 1 2020


  • catenanes
  • knots
  • links
  • weaves

ASJC Scopus subject areas

  • Structural Biology
  • Biochemistry
  • Materials Science(all)
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Inorganic Chemistry


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