We have quantum chemically investigated the structure, stability, and bonding mechanism in higihly aggregated alkali-metal salts of bismuthanediide anions [RBi](2-) using relativistic density functional theory (DFT, at ZORA-BP86/TZ2P) in combination with a quantitative energy decomposition analysis (EDA). Our model systems are alkali-metal-supported bismuth polyhedra [(RBi)(n)M2n-4](4-) with unique interpenetrating shells of a bismuth polyhedron and an alkali-metal superpolyhedron. Furthermore, we have analyzed the trianionic inclusion complexes [M'@{(RBi)(n)M2n-4}](3-) involving an additional endohedral alkalimetal ion M'. The main objective is to assist the further development of synthetic approaches toward this class of compounds. Our analyses led to electron-counting rules relating, for example, the number of bonding orbitals (N-bond) of the cage molecules [(RBi)(n)M2n+Q](Q) to the number of bismuth atoms (n(Bi)), alkali-metal atoms (n(M)), and net charge Q as N-bond = n(Bi) + n(M) - Q(R = one-electron donor ligand; M = alkali metal; n = 4-12; Q = -4, -6, -8). Finally, on the basis of our findings, we predict the next members in the S-fold symmetrical row of alkali-metallobismaspheres with a macroicosahedral arrangement.