The sharing of edges and particularly faces by two anion polyhedra decreases the stability of an ionic structure. Sharing of corners does not decrease stability as much, so (for example) octahedra may share corners with one another.
The decrease in stability is due to the fact that sharing edges and faces places cations in closer proximity to each other, so that cation-cation electrostatic repulsion is increased. The effect is largest for cations with high charge and low C.N. (especially when r+/r- approaches the lower limit of the polyhedral stability). Generally, smaller elements fulfill the rule better.
As one example, Pauling considered the three mineral forms of titanium dioxide, each with a coordination number of 6 for the  cations. The most stable (and most abundant) form is rutile, in which the coordination octahedra are arranged so that each one shares only two edges (and no faces) with adjoining octahedra. The other two, less stable, forms are brookite and anatase, in which each octahedron shares three and four edges respectively with adjoining octahedra.