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Title of Journal: J Math Chem

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Abbravation: Journal of Mathematical Chemistry

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Springer Netherlands

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DOI

10.1007/s10910-008-9487-z

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1572-8897

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The architecture of Platonic polyhedral links

Authors: Guang Hu XinDong Zhai Dan Lu WenYuan Qiu
Publish Date: 2008/11/04
Volume: 46, Issue: 2, Pages: 592-603
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Abstract

A new methodology for understanding the construction of polyhedral links has been developed on the basis of the Platonic solids by using our method of the ‘nbranched curves and mtwisted doublelines covering’ There are five classes of platonic polyhedral links we can construct the tetrahedral links the hexahedral links the octahedral links the dodecahedral links the icosahedral links The tetrahedral links hexahedral links and dodecahedral links are respectively assembled by using the method of the ‘3branched curves and mtwisted doublelines covering’ whereas the octahedral links and dodecahedral links are respectively made by using the method of the ‘4branched curves’ and ‘5branched curves’ as well as ‘mtwisted doublelines covering’ Moreover the analysis relating topological properties and link invariants is of considerable importance Link invariants are powerful tools to classify and measure the complexity of polyhedral catenanes This study provides further insight into the molecular design as well as theoretical characterization of the DNA polyhedral catenanes

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