Isogonal piecewise-linear embeddings of 1-periodic knots and links, and related 2-periodic chain-link and knitting patterns

Michael O'Keeffe, Michael M.J. Treacy

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Families of 1- and 2-periodic knots and weavings that have isogonal (vertex-transitive) piecewise-linear embeddings are described. In these structures there is just one thread, or multiple threads with parallel or collinear axes. The principal structures are a large family of 1-periodic knots and related multi-thread infinite links, knitting patterns and chain-link weaving. The relevance to synthetic chemistry is described in terms of targets for designed synthesis such as mechanically interlocked polymers.

Original languageEnglish (US)
Pages (from-to)234-241
Number of pages8
JournalActa Crystallographica Section A: Foundations and Advances
Volume78
DOIs
StatePublished - May 1 2022

Keywords

  • isogonal structures
  • knitting patterns
  • knots
  • links
  • mechanically interlocked polymers
  • weaves

ASJC Scopus subject areas

  • Structural Biology
  • Biochemistry
  • General Materials Science
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Inorganic Chemistry

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