Nitrogen molecules are the focus of much attention for their potential as high-energy density materials. The usefulness of such molecules as energy sources depends on the stability of the molecules with respect to dissociation. Many such molecules dissociate too easily to be a stable fuel, and the reasons for such instability are related to the details of structure and bonding of the molecule. Such details will be examined for isomers of the molecule N-20. N-20 has a highly symmetric isomer in which the 20 atoms occupy the vertexes of a dodecahedron. This isomer is a cage molecule in which all of the faces are regular pentagons that have interior angles of 108degrees. These angles are very close to the known bond angles in very stable nitrogen compounds such as ammonia. Such a structure with only pentagons should provide an ideal bonding environment for three-coordinate nitrogen. However, by use of theoretical calculations including density-functional theory and fourth-order perturbation theory, along with the Dunning correlation-consistent basis sets, it will be shown that dodecahedral N-20 is not the most stable cage for N-20. The reasons why will be discussed in terms of the structure and bonding of the molecules.