The cyclic hydrocarbon polyenes with the general formula CNHN are called N-annulenes. In this paper, we discover that Gentile oscillators and N-annulenes in the Huckel approximation have the same energy spectra determined by the contact points of a regular polygon inscribed on a circle. This correspondence is derived from the symmetry of a C(n + 1) rotational group and dihedral group Dih(N). On the basis of their energy spectra, we further demonstrate that these two kinds of systems have the same partition functions and, thus, the same thermodynamics properties. N-annulenes can, therefore, be viewed as the natural realization of Gentile systems.