Electron partition schemes are a beneficial means to systematize bonding networks and to identify structure-bonding relationships in polar intermetallics. One prolific class of polymetal networks with simple counterions is the broad family of transition-metal (T)-centered rare-earth metal (R) cluster halides (X), which can be isolated or condensed to oligomers and chains. While the electronic structures of R cluster monomers and chains encapsulating T atoms have been studied systematically, the band structures of oligomers, in particular, the most frequent Friauf-type {T4R16} tetramers, have been investigated to a lesser extent. Therefore, the band structures of prototypical compounds with {T4R16}-type tetramers, while maintaining different compositions, were analyzed employing density functional theory based methods. Furthermore, these theoretical examinations provide insight into the origin of the 15 electron rule, which is significant for this class of compounds and correlates with the closed-shell configurations for these structures. Additional research focused on the band structure of monoclinic {Ru4Gd16}Br23, which is composed of rhomboid-shaped {Ru4Gd16} tetramers.