Survey of Tetrahedral Structures

Structures built from tetrahedral AX$_{4}$ groups that share some or all of their X atoms may be classified according to the numbers of tetrahedra to which the X atoms belong. If v$_{x}$ is the number of X atoms of each AX$_{4}$ group in a structure of composition A$_{m}$ X$_{n}$ which are common to x such groups (that is, x is the coordination number of X) then $\Sigma $v$_{x}$ = 4 and $\Sigma $(v$_{x}$/x) = n/m. The solutions of these equations for any composition A$_{m}$ X$_{n}$ may be examined systematically. The present survey is restricted to structures which can be constructed from regular tetrahedral AX$_{4}$ groups, all of which share their X atoms in the same way and have no X-X separations shorter than the edge of a tetrahedron. A study is made of the types of possible structure, finite, one-, two- or three-dimensional, and the emphasis is on the topology rather than the geometry of the structures.