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It has been elegantly accepted that oxygen adsorption onto the Cu(110) surface induces an expansion of the first layer-spacing and a contraction of the second in addition to the alternative Cu[001] row that is either missing or forming the O-Cu-O row of high protrusions. However, it needs yet to clarify the vertical position of the oxygen and the hard-sphere models of added-, missing- and buckled-row. Here we justify that all the structures determined and all the models developed so far are correct in the sense of numerical solutions and phenomenological descriptions. A tetrahedral bond configuration of sp-orbital hybridization developed recently, however, may serve as a criterion to identify the physical solution that could account consistently for the observations using scanning tunneling microscopy/spectroscopy (STM/S), X-ray diffraction (XRD), and ultraviolet photoelectron spectroscopy (UPS). [ABSTRACT FROM AUTHOR]