The New Euler Characteristics Of DNA Polyhedra

A new methodology based on the Seifert construction has been developed to study polyhedral links by new Euler characteristics, which reveals the intrinsic properties of DNA polyhedra. It is shown that through a relationship between faces of the underling polyhedron and the component number of the polyhedral link, the new Euler characteristic can be calculated and thereby extend the Eulers theorem to DNA polyhedra embedded in torus or surfaces with higher genus. We further discuss the application of new Euler characteristics in DNA nanotechnology, with particular reference to some potential DNA polyhedra that consist of edges both with even and odd half-twists.