Isogonal piecewise‐linear embeddings of 1‐periodic knots and links, and related 2‐periodic chain‐link and knitting patterns. Issue 3 (4th April 2022)

• Record Type: Journal Article
• Authors: O'Keeffe, Michael; Treacy, Michael M. J.
• Is Part Of: Acta crystallographica. Volume 78:Issue 3(2022)
• Page Start: 234
• Page End: 241
• Publication Date: 2022-04-04
• Subjects: knots -- weaves -- isogonal structures -- links -- knitting patterns -- mechanically interlocked polymers; Crystallography -- Periodicals; Condensed matter -- Periodicals; 548
• DOI: 10.1107/S205327332200198X
• Languages: English
• ISSNs: 2053-2733

Abstract

Abstract : 1‐ and 2‐periodic structures are described built from single threads, or from multiple threads with parallel or collinear axes. The work has relevance to the manufacture of mechanically interlocked polymers. 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.