B3LYP/6-31G* computations predict the relative energies and stabilities of the endohedral (XΓ20H20) and exohedral (XC20H20) dodecahedrane complexes (X = H+, H, N, P, C-, Si-, O+, S+). H+ does not bind endohedrally but bridges a C-C bond exohedrally; the proton affinity is 185.3 kcal/mol. Except for O+, all other guest species (H, N, P, C-, Si-, S+) are minima at the cage center. The H-atom inclusion energy is similar to that of helium (36.3 vs 38.0 kcal/mol), whereas the other endohedral complexes have much higher inclusion energies (125-305 kcal/mol). In all cases, the endohedral complexes are energetically less favorable than their exohedral isomers. C20H21 has a cage-ruptured structure, whereas N, P, and their isoelectronic analogues have exohedral structures and bind as doublet states to broken cage C-C bonds. Endohedral H, N, C-, O+, and S+ preserve their unencapsulated ground states, whereas P and Si- interact strongly with the cage and lose their atomic ground-state character.