The equilibrium geometries and frequencies of endohedral complexes between H, He, Ne, Ar, Li, Li+, Be, Be+, Be2+, Na, Na+, Mg, Mg+, and Mg2+ and dodecahedrane (X@C20H20) were computed at B3LYP/6-311+G(d,p). The majority have I-h minima; the exceptions, X@C20H20 (X = Be, Be+, Be2+), have C-5nu symmetry With X localized against an inner cage face. Cage C-C bonds shorten slightly (<0.01 Angstrom) and cage C-H bonds lengthen slightly (less than or equal to 0.02 Angstrom) in the series: M2+@C20H20 --> M+@C20H20 --> M@C20H20 (M = Li, Na, Be, Mg). These subtle changes in dodecahedrane geometry are due to donation of electron density from the encapsulated metal atom into the C-C bonding and C-H antibonding endohedral complex HOMO, which has a structure closely resembling the LUMO (A(1g)) of dodecahedrane. The zero point-corrected inclusion energies of Li+@C20H20 (I-h; -12.7 kcal/mol), Be+@C20H20 (C-5nu; -1.3 kcal/mol), Be2+@C20H20 (C-5nu; -236.3 kcal/mol) and Mg2+@C20H20 (I-h; -118.0 kcal/mol) are exothermic relative to their isolated components. However, all the endohedral dodecahedrane complexes are higher in energy than their corresponding exohedral isomers. Endohedral He and Li+ chemical shifts are 0.9 and 1.9 ppm, respectively. M@C20H20 (M = Li, Na, Be, Mg) species possess lower first ionization potentials than the Cs atom (3.9 eV) and, therefore, are "superalkalis". Removal of dodecahedrane hydrogens can increase endohedral complex stability significantly. Thus, endohedral beryllium in the beryllocene complex, Be@C20H20 (D-5d) is 75.3 kcal/mol more stable than its isolated components, in contrast with Be@C20H20 which is unstable by 127.7 kcal/mol. Dodecahedrane, He@C20H20 and Li@C20H20 B3LYP/6-31G(d) and B3LYP/6-311+G(d,p) absolute energies did not change significantly (<0.31 kcal/mol) when computed using either a pruned (75,302) or pruned (99,590) integration grid; with the addition of zero point energy the maximum deviation was less than 0.53 kcal/mol.