In the formation of binary compounds, heteroatomic interactions are generally expected to play the leading role in providing stability. In this Article, we present a series of gallides, T4Ga(5) (T = Ta, Nb, and Ta/Mo), which appear to defy this expectation. Their complex crystal structures represent a new binary structure type (to the best of our knowledge),, which can be visualized in terms of a host lattice of T@T-8 body centered cubic (bcc) clusters linked through face-capping Ga-2 dumbbells to form a primitive cubic framework. The cubic spaces that result are alternately filled by distorted T pentagonal dodecahedra (sharing atoms with the host lattice) and dimers of bcc fragments, leading to a root 2 x root 2 x 2 supercell of the host framework structure. Ga tetrahedra and icosahedral units fill the remaining void spaces. Underlying these structural features is a strong tendency for homoatomic clustering of Ta and Ga, which is evident in all of the coordination polyhedra. Electronic structure calculations using density functional theory (DFT) and DFT-calibrated Huckel models reveal possible origins for this elemental segregation and the factors stabilizing the structure as a whole. A deep pseudogap is present at the Fermi energy of Ta4Ga5 (as well as at that of Nb4Ga5), corresponding to the near-optimization of Ta-Ta and Ta-Ga interactions. This pseudogap emerges as a result of the ability of extensive Ta-Ta bonding to provide local 18-electron configurations to the Ta atoms, despite the electron concentration being only 8.75 electrons per Ta atom. Support for these Ta-Ta interactions is provided by Ga bridging atoms, whose valence orbitals low number of angular nodes confers preferential stabilization to Ta-Ta bonding functions over antibonding ones. The observed spatial separation of the structure into Ta and Ga domains occurs as a consequence of the Ga atoms being pushed toward the periphery of the Ta clusters to play this supporting role.