Synthesis and structural characterization of the new compounds R2Zn1-xGe6 (R = La-Nd, Sm, Gd-Ho) is reported. A structural change was revealed along this series by careful analysis of single-crystal X-ray diffraction data. For light rare earths up to Tb the orthorhombic oS72-Ce-2(Ga0.1Ge0.9)(7) model was established; instead, the Dy compound represents a new structure type (P2(1)/m, mP34, Z = 4, a = 7.9613(3) angstrom, b = 8.2480(4) angstrom, c = 10.5309(5) angstrom, beta = 100.861(1)degrees) being a superstructure of the mS36-La2AlGe6 prototype. The established structural models support the increase of Zn deficiency along the series, suggested by microprobe analysis, and its key role in governing structural changes. The vacancy ordering criterion was applied as a successful approach to find a general scheme including the structures of the similar to R2MGe6 compounds known up to now (R = rare-earth metal, M = transition metal, Mg, Al, Ga) and highlighting the subtle structural differences within this family. According to this scheme, these structures are obtained from a common aristotype (oS20-SmNiGe3) via symmetry reduction based on groupsubgroup relations accompanied by ordering of vacancies. This approach was optimized with the help of the ToposPro software and extended to the R2Zn3Ge6 series, enriched with new members (R = Sm, Gd-Ho) during this work. Electronic structure calculations on La2ZnGe6 confirm the presence of infinite covalent germanium zigzag chains and three-bonded corrugated layers connected via Zn atoms to form a polyanionic network stabilized by La atoms.