Single-phase polycrystalline samples of RBa2Cu2.9Zn0.1Oy (R = Y, Nd, Gd, Er, and Tm) (ZnR123) were synthesized using the standard solid-state reaction method. They were characterized by X-ray powder diffraction (XRD) and scanning electron microscope. XRD shows that all samples consist essentially of a single phase and retain the orthorhombic structure. The structure of the samples was refined by the Rietveld method with the help of the bond valence sum method. The variation of the lattice parameters and some meaningful bond angles and lengths with the ionic radius are discussed. In these compounds, the variations of the buckling angles Cu2–O(2,3)–Cu2 and Cu2–Cu2–O(2,3) are unique: the bond angles Cu2–O3–Cu2 and Cu2–Cu2–O2 increase, whereas the bond angles Cu2–O2–Cu2 and Cu2–Cu2–O3 decrease. The variation of these bond angles brings about a strong curvature of the Cu2O plane. Furthermore, we have found tree fixed triangles formed by the Cu2, O2, and O3 atoms in addition to another fixed triangle O1–Ba–O1 observed for the first time. BVS of Cu2 atom shows a specific and unique variation compared with other compounds.