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【期刊论文】Molecular design of Goldberg polyhedral links
邱文元, Wen-Yuan Qiu *, Xin-Dong Zhai
Journal of Molecular Structure: THEOCHEM 756 (2005) 163-166,-0001,():
-1年11月30日
A new method for understanding the construction of polyhedral links has been developed on the basis of the novel structure of HK97 capsid and the classification of Goldberg polyhedra. Polyhedral links, the interlinked and interlocked architectures, have been solved by analyzing and characterizing the topological structure of the two types of polyhedral links, which are RnC1ZRnC10(2nC1) and RnC1ZRnC20n. Where, nZ1, 2,., R1Z12 and R represents the number of the interlocked rings. Our results show that these two types of polyhedral links both have I symmetry and therefore are said to possess chirality.
Knot theory, Goldberg polyhedra, Polyhedral links, Symmetry, Chirality, Protein catenane
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【期刊论文】The complexity of Platonic and Archimedean polyhedral links
邱文元, Guang Hu·Wen-Yuan Qiu·Xiao-Sheng Cheng·Shu-Ya Liu
J Math Chem (2010) 48: 401-412,-0001,():
-1年11月30日
A mathematical methodology for understanding the complexity of Platonic and Archimedean polyhedral links has been developed based on some topological invariants from knot theory. Knot invariants discussed here include rossing number, unknotting number, genus and braid index, which are considered significant in viewofDNAnanotechnology. Our results demonstrate that the braid index provides the most structural information; hence, it can be used, among four knot invariants, as the most useful complexity measure. Using such an invariant, it indicates that the complexity of polyhedral links is directed by the number of their building blocks. The research introduces a simple but important concept in the theoretical characterization and analysis of DNA polyhedral catenanes.
Platonic polyhedra·Archimedean polyhedra·Polyhedral links·Knot invariants·Complexity measures·DNA catenanes
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【期刊论文】Extended Goldberg polyhedral links with even tangles
邱文元, Guang, HU and Wen-Yuan, QIU *
MATCH Commun. Math. Comput. Chem. 61(2009)737-752,-0001,():
-1年11月30日
A new methodology for understanding the construction of polyhedral links has been developed on the basis of 4-regular polyhedra and knot theory. In the method, we utilize uniform 2n-tangles (n is an integer) to cover all vertexes of Extended Goldberg polyhedra, and many infinite series of interlinked and interlocked architectures have been assembled. The growth rule of links with tangle of |n|=1 and a class of topological transformation depending on the number of n are systematic enumerated. Our study reveals that these novel structures all have I symmetry and each belongs to a given topological configuration, D or L. Moreover, they provide some potential models for protein and DNA cages which have chirality.
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【期刊论文】Extended Goldberg polyhedra
邱文元
,-0001,():
-1年11月30日
A new methodology for understanding the construction of Extended Goldberg polyhedra has been developed on the basis of Goldberg polyhedra by using our methods of the ‘spherical rotating’ and the ‘spherical stretching’. The spherical rotating describes the deformation of rotating polygons on a sphere; the spherical stretching depicts the deformation of stretching spaces between polygons on a sphere. Our results show that these Extended Goldberg polyhedra are a kind of novel geometrical objects of icosahedral symmetry and are considered to explain some viral capsids.
Goldberg polyhedra,, Spherical rotating,, Spherical stretching,, Symmetry,, virus structure
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