The D mh symmetric H x q rings, H 5 -(D 5h , D 4h ), H 5 + (C 2V ), H 6 (D 6h , D 5h ), H 7 + (D 7h , D 6h ), H 8 2+/2-(D 8h ), H 9 + (D 3h ), H 9 -(D 9h , D 8h ), and H 10 (D 10h , D 9h ) are considered as possible analogs of the Hu ¨ckel 4n + 2 electron aromatic annulene systems. While aromatic character (due to ring current effects) is indicated by the magnetic susceptibility exaltations (Λ) and large magnetic susceptibility anisotropies, χ anis (derived from IGLO computations of the magnetic properties), most of these hydrogen ring systems are higher order saddle points. The exceptions are transition structures: H 6 (D 6h ), which can be compared with benzene, and H 10 (D 10h ) which is even less favorable energetically. On the basis of energetic, structural, and magnetic criteria, aromaticity can result from cyclic delocalization of σas well as π-electrons. On the basis of the diamagnetic exaltations, "spherical aromaticity" is illustrated by H 6 2and H 8 , both with O h symmetry and eight σ-electrons as well as H 4 2+ with T d symmetry and only two σ-electrons, even though these species are artificial, higher order saddle points. The Hu ¨ckel 4n electron antiaromatic H 3 -(D 3h ), H 4 (D 4h ), H 5 + (D 5h , D 4h ), and H 8 (D 8h ) triplet states have been computed. Both H 4 (D 4h ) and H 8 (D 8h ) have negative (unfavorable) energies of concert relative to two H atoms and the appropriate number of H 2 molecules.