In this paper we set up a topological model which can be used to describe closed circular (cc) DNAs on the basis of Seifert construction in knot theory. We visually prove that the backbones of T2n-ccDNAs (n=1,2,…) in the crystal which are topological chiral possess the point symmetry group C and that the backbones of T2n-ccDNAs in solution which are topological achiral possess the point symmetry groups Sn2, Sn and S2n. Topological achirality leads us to believe that right handed DNA can be flipped over into a left handed hcilx. Further it also proveides a sound basis for the investigation of this surprising manifestation of DNA supereoiling. Replication. transcription and recombination.