Nitrogen molecules have been extensively studied for their potential as high energy density materials (HEDM). One of the major issues in the study of N-x all-nitrogen molecules is the determination of stable structures. In this study, various cage isomers of N-24, N-30, and N-36 are examined for the purposes of determining relative thermodynamic stability. Trends in thermodynamic stability make possible the identification of structural features that lead to stable molecules. All of the molecules in this study have three-coordinate nitrogen with all N-N single bonds. Thermodynamic stability is determined by theoretical calculations employing Hartree-Fock theory (HF), density functional theory (B3LYP), and Moller-Plesset perturbation theory (up to MP4). The correlation-consistent basis sets of Dunning are employed. The major result of this study is the identification of cylinder-shaped molecules that are substantially more stable than more spherically shaped isomers.