We present transition metal-embedded (T@Ga n ) endohedral Gaclusters as a favorable structural motif for superconductivity and develop empirical, molecule-based, electron counting rules that govern the hierarchical architectures that the clusters assume in binary phases. Among the binary T@Ga n endohedral cluster systems, Mo 8 Ga 41 , Mo 6 Ga 31 , Rh 2 Ga 9 , and Ir 2 Ga 9 are all previously known superconductors. The well-known exotic superconductor PuCoGa 5 and related phases are also members of this endohedral gallide cluster family. We show that electron-deficient compounds like Mo 8 Ga 41 prefer architectures with vertex-sharing gallium clusters, whereas electron-rich compounds, like PdGa 5 , prefer edge-sharing cluster architectures. The superconducting transition temperatures are highest for the electron-poor, corner-sharing architectures. Based on this analysis, the previously unknown endohedral cluster compound ReGa 5 is postulated to exist at an intermediate electron count and a mix of corner sharing and edge sharing cluster architectures. The empirical prediction is shown to be correct and leads to the discovery of superconductivity in ReGa 5 . The Fermi levels for endohedral gallide cluster compounds are located in deep pseudogaps in the electronic densities of states, an important factor in determining their chemical stability, while at the same time limiting their superconducting transition temperatures. Although one can analyze the superconductivity, once discovered, through materials physics-based "k-space" pictures based on Fermi surfaces, energy band dispersions, and effective interactions, often it is chemists, whose viewpoint is instead from "real space" rather than k-space, who find such superconductors in the first place (1, 2). Given the difficulty in making extrapolations between the physics of superconductivity and the chemical stability of compounds that will be superconducting, there are as many strategies for finding new superconductors as there are researchers looking for them (3-5). Most such search strategies fail, because the interactions that give rise to superconductivity can also lead to competing electronic states or can be strong enough to tear potential compounds apart (6, 7).One chemical perspective for increasing the odds of finding superconductivity is to postulate that it runs in structural families. The perovskites are a well-known example of this in metal oxides, and in intermetallic compounds, the "122" ThCr 2 Si 2 structure type is a good example (8-10). It is the discovery of these new structural families of superconductors that often leads, sometimes slowly or sometimes quickly, to advances in new superconducting materials. Here we show that a previously unappreciated chemical family, the endohedral gallium cluster phases, is a favored chemical family for superconductivity. Further, we analyze the occurrence and hierarchical structures of such phases from a molecular perspective and then use that perspective to predict the existence and structure of a previously un...