Strontium titanate is seeing increasing interest in fields ranging from thin-film growth to water-splitting catalysis and electronic devices. Although the surface structure and chemistry are of vital importance to many of these applications, theories about the driving forces vary widely(1,2). We report here a solution to the 3 x 1 SrTiO3(110) surface structure obtained through transmission electron diffraction and direct methods, and confirmed through density functional theory calculations and scanning tunnelling microscopy images and simulations, consisting of rings of six or eight corner-sharing TiO4 tetrahedra. Further, by changing the number of tetrahedra per ring, a homologous series of n x 1 (n >= 2) surface reconstructions is formed. Calculations show that the lower members of the series (n <= 6) are thermodynamically stable and the structures agree with scanning tunnelling microscopy images. Although the surface energy of a crystal is usually thought to determine the structure and stoichiometry, we demonstrate that the opposite can occur. The n x 1 reconstructions are sufficiently close in energy for the stoichiometry in the near-surface region to determine which reconstruction is formed. Our results indicate that the rules of inorganic coordination chemistry apply to oxide surfaces, with concepts such as homologous series and intergrowths as valid at the surface as they are in the bulk.