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2D and 3D lattice complexes with increased self-coordination numbers Ti (i=1–3), of nearest, second and third neighbors were derived for characteristic Wyckoff sets with zero or one parameters. Structure types of adsorbed atoms in 2D or elements A in 3D and AxBy compounds are approximated to the list of lattice complexes. Covalent bonding or electronic effects of atoms such as lone electron pairs or Jahn–Teller distortion give rise to deviations from lattice complexes.