The series of isotypic compounds V8Ga41 --> V8Ga36.9Zn4.1 --> Cr8Ga29.5Zn11.2 --> Mn8Ga27.4Zn13.6 with the V8Ga41 structure type (space group R3, Z = 3) was prepared and structurally characterised by X-ray diffraction experiments (V8Ga41: a 13.9351(5), 14.8828(12); V8Ga36.9Zn4.1: a = 13.9244(7), c = 14.8660(9): Cr8Ga29.8Zn11.2: 13.7153(5), c = 14.6872(9); Mn8Ga27.4Zn13.6: a = 13.6033(6), c = 14.6058(16)). The site occupancies of the ternary compounds were refined from neutron powder-diffraction data and exposed a startling segregation of Zn and Ga, which finally resulted in the formation of separated Zn13 cluster entities-corresponding to almost ideal centred cuboctahedra or small pieces of fcc metal-in the Mn compound, which has the highest Zn content in the series. The homogeneity ranges of the underlying phases T8Ga41 xZnx were determined to be 0 < x < 4.1(3), 8.7(3) < x < 11.2(3) and 13.6(4) < x < 16.5(3) for T = V, Cr and Mn, respectively. The different ranges of composition of the phases reflect the requirement of an optimum electron concentration for a stable V8Ga41-type structure, which is in the narrow range between 159 and 165 electrons per formula unit. First-principles electronic-structure calculations could explain this fact by the occurrence of a pseudo gap in the density of states at which the Fermi level is put for this particular electron concentration. Furthermore the nature of the Zn/Ga segregation was revealed: T-Zn interactions were found to be considerably weaker than those for T-Ga. This places the Zn atoms as far as possible from the T atoms, thus leading to the formation of cuboctahedral Zn13 entities.