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Wiley, Acta Crystallographica Section a Foundations of Crystallography, a1(68), p. s187-s187, 2012

DOI: 10.1107/s0108767312096390

Wiley, Acta Crystallographica Section a Foundations of Crystallography, 4(68), p. 484-493, 2012

DOI: 10.1107/s0108767312019034

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A topological method for the classification of entanglements in crystal networksA preliminary account of this work was presented at the workshop `Topological dynamics in physics and biology' held in Pisa, 12–13 July 2011.

Journal article published in 2012 by Eugeny V. Alexandrov, Vladislav A. Blatov ORCID, Davide M. Proserpio
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

A rigorous method is proposed to describe and classify the topology of entanglements between periodic networks if the links are of the Hopf type. The catenation pattern is unambiguously identified by a net of barycentres of catenating rings with edges corresponding to the Hopf links; this net is called the Hopf ring net. The Hopf ring net approach is compared with other methods of characterizing entanglements; a number of applications of this approach to various kinds of entanglement (interpenetration, polycatenation and self-catenation) both in modelled network arrays and in coordination networks are considered.