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 Huckel 4n + 2 electron aromatic annulene systems. While aromatic character (due to ring current effects) is indicated by the magnetic susceptibility exaltations (Lambda) and large magnetic susceptibility anisotropies, chi(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 sigma- as well as pi-electrons. On the basis of the diamagnetic exaltations, "spherical aromaticity" is illustrated by H-6(2-) and H-8, both with O-h symmetry and eight sigma-electrons as well as H-4(2+) With T-d symmetry and only two sigma-electrons, even though these species are artificial, higher order saddle points. The Huckel 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.