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

Isogonal piecewise‐linear embeddings of 1‐periodic knots and links, and related 2‐periodic... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Foundations and Advances Wiley

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

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Publisher
Wiley
Copyright
Copyright © 2022 Wiley Subscription Services, Inc., A Wiley Company
eISSN
2053-2733
DOI
10.1107/s205327332200198x
Publisher site
See Article on Publisher Site

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.

Journal

Acta Crystallographica Section A: Foundations and AdvancesWiley

Published: May 1, 2022

Keywords: knots; weaves; isogonal structures; links; knitting patterns; mechanically interlocked polymers

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