A new method for studying cages and channels in crystal structures is implemented into the program package TOPOS. The method is based on the concept of Voronoi-Dirichlet partition of crystal space. All X-ray investigated ternary and quaternary lithium-containing inorganic compounds (822 compounds LiaXbOz and 1349 compounds Li(a)X1bX2(c)O(z), where X, X1 and X2 are any chemical elements) are analyzed and the dimensionality of channel systems, providing transport of lithium ions, is determined. For all compounds the migration maps (conduction patterns) characterizing the conduction channel systems of dimensions 1, 2 or 3, are constructed. We have found the coordinates of lithium atoms as centres of the cages obtained, and the Coordinates fit the experimental data accurate to 0.6 angstrom. Totally, 277 compounds with infinite systems of conduction channels are invented. Out of them, 251 compounds (126 structural types) were mentioned in the literature as solid electrolytes, the other 26 (24 Structural types) can be considered as potential ionic conductors with 1D (for 16 types), 2D (for 2 types) or 3D (for 6 types) conductivity. (C) 2008 Elsevier B.V. All rights reserved.