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Updated: Jul 9, 2025

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Published on: February 7, 2017
Isogonal 2-periodic polycatenanes: chain mail
Michael O'Keeffe1, Michael M J Treacy2
1School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287, USA.
Abstract:
For 2-periodic polycatenanes with isogonal (vertex-transitive) embeddings, the basic units linked are torus knots and links including the unknots (untangled polygons). Twenty-four infinite families have been identified, with hexagonal, tetragonal or rectangular symmetry. The simplest members of each family are described and illustrated. A method for determining the catenation number of a ring based on electromagnetic theory is described.
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