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A new Euler formula and its characterizaion of DNA polyhedra

This paper studies the law of component number of DNA polyhedral links from mathematical and chemical viewpoints. The topological properties of extended Platonic polyhedral links, including component number, Seifert circle number, crossing number, characteristic λ, characteristic Q,are characterized intrinsically.We extend the polyhedral links with even half-twistsedges to the ones with odd half-twistsedges, which is helpful for experimenter to design and synthesize various practical DNA polyhedra. Our study indicates that there are some rules to follow for more DNA polyhedra, providing reference materials and some extended examples.