A recently discovered high-Tc cuprate superconductor Ba2CuO4-δ exhibits exceptional Jahn-Teller distortion, wherein the CuO6 octahedrons are compressed along the c axis. As a consequence, the O vacancies prefer to reside in the CuO2 plane, but the exact structure is not known. By combining first-principles total energy calculation with the automated structure inversion method, the effective cluster interactions of O vacancies are mapped out. Around δ=0.8, where the 73K superconductivity was observed experimentally, we predict that the ordered O vacancies slice the CuO2 plane into not only 1D chains and but also two-leg ladders. A Monte Carlo simulation is performed based on the effective cluster interaction model, showing that such an ordering pattern is stable up to ~900 K. Our results put forth a concrete structural basis to discuss the underlying superconducting mechanism.2 Main Text:High-Tc superconductivity in cuprates is commonly spawned in the intact two-dimensional CuO2 plane [1][2][3][4][5][6]. However, a new cuprate superconductor Ba2CuO4-δ appears to be an exception [7]. Ba2CuO4-δ crystallizes into the typical 214 layered perovskite structure [ Fig. 1(a)], but the CuO6 octahedrons are largely compressed along the c axis, making the in-plane Cu-O bonds weaker than the out-of-plane ones. Consequently, in contrast to the apical substitution as typically observed in other high-Tc cuprates [3][4][5][6], here the O vacancies prefer to be created in the CuO2 plane [8,9]. Surprisingly, superconductivity emerges at a very high concentration of in-plane O vacancies, when the 2D parent lattice has been strongly disrupted, and the superconducting transition temperature reaches as high as 73 K around δ=0.8.At present, the in-plane O vacancy structure is still largely unknown except for the δ=1 limit, i.e. Ba2CuO3 [8]. This stoichiometric compound as a quasi-1D Mott insulator consists of paralleled (-O-Cu-O-) chains. One can reversely consider that superconductivity emerges from Ba2CuO3+γ around γ=0.2, when excess O atoms link the 1D chains, which appears to play an important role in the 73 K superconductivity, because in other quasi-1D cuprates with charge doping only, such a high Tc has never been observed.[9-12] An interesting observation is that the atomic structure of Ba2CuO3 can be viewed as long-range ordering of in-plane O vacancies in Ba2CuO4. Ba2CuO3 shares exactly the same lattice as Ba2CuO4, with only slight changes of the lattice constants (Tab. I). The O atoms are missing along all the unidirectional (-O-Cu-O-) arrays, like cutting either the warp or the weft of a fabric. The coordinates of the remaining atoms stay almost unchanged.