Fullerenes that violate the isolated pentagon rule are too reactive and were obtained only as endoor exohedral derivatives. Density functional theory using the B3LYP hybrid density functional was applied to investigate the electronic and structural properties of the ten smallest tetrahedral (Td or T point group) fullerenes containing four directly fused pentagon-triples. The influence of nitrogen doping and exohedral hydrogenation of the four reactive sites was also analyzed. Nucleus independent chemical shifts values computed using B3LYP/6-31G(d) are used as global and local aromaticity probe. The global strain energy is evaluated in terms of the pyramidalization (POAV) angle. The results show that the stability increases with the elimination of the energetically unfavorable strain.