Architecture of Platonic and Archimedean polyhedral links

摘要

A new methodology for understanding the construction of polyhedral links has been developed on the basis of the Platonic and Archimedean solids by using our method of the 'three-cross-curve and double-twist-line covering'.There are five classes of polyhedral links that can be explored:the tetrahedral and truncated tetrahedral links;the hexahedral and truncated hexahedral links;the dodecahedral and truncated dodecahedral links;the truncated octahedral and icosahedral links.Our results show that the tetrahedral and truncated tetrahedral links have T symmetry;the hexahedral and truncated hexahedral links,as well as the truncated octahedral links,O symmetry;the dodecahedral and truncated dodecahedral links,as well as the truncated icosahedral links,I symmetry,respectively.This study provides further insight into the molecular design,as well as theoretical characterization,of the DNA and protein catenanes.