Four complex intermetallic compounds BaAu_6±xGa_6±y (x = 1, y = 0.9) (I), BaAu_6±xAl_6±y (x = 0.9, y = 0.6) (II), EuAu_6.2Ga_5.8 (III), and EuAu_6.1Al_5.9 (IV) have been synthesized, and their structures and homogeneity ranges have been determined by single crystal and powder X-ray diffraction. Whereas I and II originate from the NaZn₁₃-type structure (cF104–112, Fm3̅c), III (tP52, P4/nbm) is derived from the tetragonal Ce₂Ni₁₇Si₉-type, and IV (oP104, Pbcm) crystallizes in a new orthorhombic structure type. Both I and II feature formally anionic networks with completely mixed site occupation by Au and triel (Tr = Al, Ga) atoms, while a successive decrease of local symmetry from the parental structures of I and II to III and, ultimately, to IV correlates with increasing separation of Au and Tr on individual crystallographic sites. Density functional theory-based calculations were employed to determine the crystallographic site preferences of Au and the respective triel element to elucidate reasons for the atom distribution (“coloring scheme”). Chemical bonding analyses for two different “EuAu₆Tr₆” models reveal maximization of the number of heteroatomic Au–Tr bonds as the driving force for atom organization. The Fermi levels fall in broad pseudogaps for both models allowing some electronic flexibility. Spin-polarized band structure calculations on the “EuAu₆Tr₆” models hint to singlet ground states for europium and long-range magnetic coupling for both EuAu_6.2Ga_5.8 (III) and EuAu_6.1Al_5.9 (IV). This is substantiated by experimental evidence because both compounds show nearly identical magnetic behavior with ferromagnetic transitions at T_C = 6 K and net magnetic moments of 7.35 μ_B/f.u. at 2 K. The effective moments of 8.3 μ_B/f.u., determined from Curie–Weiss fits, point to divalent oxidation states for europium in both III and IV.