Double–link expandohedra: a mechanical model for expansion of a virus

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Kovács F., Tarnai T., Guest S. D. and Fowler P. W. 2004Double–link expandohedra: a mechanical model for expansion of a virusProc. R. Soc. Lond. A.4603191–3202http://doi.org/10.1098/rspa.2004.1344SectionRestricted accessDouble–link expandohedra: a mechanical model for expansion of a virus F. Kovács F. Kovács Research Group for Computational Structural Mechanics, Hungarian Academy of Sciences, Budapest, Müegyetem rkp. 3, 1521, Hungary Google Scholar Find this author on PubMed Search for more papers by this author , T. Tarnai T. Tarnai Department of Structural Mechanics, Budapest University of Technology and Economics, Budapest, Müegyetem rkp. 3, 1521, Hungary Google Scholar Find this author on PubMed Search for more papers by this author , S. D. Guest S. D. Guest Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK () Google Scholar Find this author on PubMed Search for more papers by this author and P. W. Fowler P. W. Fowler Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD, UK Google Scholar Find this author on PubMed Search for more papers by this author F. Kovács F. Kovács Research Group for Computational Structural Mechanics, Hungarian Academy of Sciences, Budapest, Müegyetem rkp. 3, 1521, Hungary Google Scholar Find this author on PubMed Search for more papers by this author , T. Tarnai T. Tarnai Department of Structural Mechanics, Budapest University of Technology and Economics, Budapest, Müegyetem rkp. 3, 1521, Hungary Google Scholar Find this author on PubMed Search for more papers by this author , S. D. Guest S. D. Guest Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK () Google Scholar Find this author on PubMed Search for more papers by this author and P. W. Fowler P. W. Fowler Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 November 2004https://doi.org/10.1098/rspa.2004.1344AbstractDouble–link expandohedra are introduced: each is constructed from a parent polyhedron by replacing all faces with rigid plates, adjacent plates being connected by a pair of spherically jointed bars. Powerful symmetry techniques are developed for mobility analysis of general double–link expandohedra, and when combined with numerical calculation and physical model building, they demonstrate the existence of generic finite breathing expansion motions in many cases. For icosahedrally symmetric trivalent parents with pentagonal and hexagonal faces only (fullerene polyhedra), the derived expandohedra provide a mechanical model for the experimentally observed swelling of viruses such as cowpea chlorotic mottle virus (CCMV). A fully symmetric swelling motion (a finite mechanism) is found for systems based on icosahedral fullerene polyhedra with odd triangulation number, T ⩽ 31, and is conjectured to exist for all odd triangulation numbers. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Kong F, Liu J, Ding H and Gao G (2022) Type Synthesis of Modular Polyhedral Mechanisms Based on the Generalized Mechanism Models of Regular Polyhedron, Journal of Mechanical Design, 10.1115/1.4056079, 145:2, Online publication date: 1-Feb-2023. 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Guest S and Fowler P (2005) A symmetry-extended mobility rule, Mechanism and Machine Theory, 10.1016/j.mechmachtheory.2004.12.017, 40:9, (1002-1014), Online publication date: 1-Sep-2005. This Issue08 November 2004Volume 460Issue 2051 Article InformationDOI:https://doi.org/10.1098/rspa.2004.1344Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/11/2004Published in print08/11/2004 License: Citations and impact Keywordsvirus structuresmechanismpolyhedrasymmetry