Mixed metal-semiconductor clusters of the form Bi2Sin-2 and Bi2Gen-2, n = 3-8, 12, are studied theoretically by ab initio methods including density functional theory with the hybrid B3LYP functional, second-order perturbation, and coupled cluster CCSD(T) theory using the doubly polarized TZV2P basis sets. These clusters are characterized by high stability and symmetry and relatively large highest occupied-lowest unoccupied molecular orbital (HOMO-LUMO) energy gaps. It is shown that the lower energy structures of these clusters and their bonding and electronic characteristics are fully compatible with very powerful stability rules and structural laws similar to the ones for the corresponding isovalent boranes, carboranes, and bisboranes. This is particularly true for the Bi2Gen-2 Clusters, the global minima of which are identical to the ones of the corresponding isovalent carboranes and bisboranes, obtained by proper substitutions from the corresponding dianions. The Bi2Sin-2 clusters for it > 8, although isolobal to the homologous Si-n(2-) Clusters, are not fully isolobal with the corresponding boranes, carboranes, and bisboranes as the n = 3-8 clusters. For the Bi2Sin-2 clusters with n <= 8, a strange odd-even effect is observed. For the even-n Bi2Sin-2 clusters, in contrast to those of odd-n, the structures obtained from the Si-n(2-) dianions through the so-called "boron connection" compete with those obtained from substitutions on the corresponding neutral cluster structures. The even-n Bi2Sin-2 clusters are fluxional or isomerizable The Bi2Si4 cluster in particular is fluxional and structurally similar to the corresponding Si-6 cluster. The differences between the Bi2Sin-2 and Bi2Gen-2 clusters are attributed mainly to the inert pair effect in Bi2Gen-2. For this reason, although the lowest energy structure of the Bi2Si10 cluster has relatively low (C-s) symmetry derived from the corresponding Si-12(2-) structure, the homologous Bi2Ge10 cluster is characterized by high D-5d symmetry obtained from the Ge-12(2-) dianion Of full icosahedral symmetry, similar to the corresponding (B12H12)(2-) borane. The present rationalization of the silicon/germanium-bismuth clusters is very promising for deeper understanding and future functionalization toward useful chemical and technological applications.