Survey of octahedral structures AXn and A2Xn

Structures built from octahedral AX6 groups that share some or all of their X atoms may be classified according to the numbers of octahedra to which the X atoms belong. If vx is the number of X atoms of each AX6 group in a structure of composition AmXn which are common to xsuch groups (that is, x is the coordination number of X) then hvx — 6 and lL{vx/x) — n/m.The solutions of these equations for any composition AmX^ may be examined systematically. The present survey is restricted to structures in which m = 1 or 2 which can be constructed from regular octahedral AX6 groups all of which share their X atoms in the same way and have no X-X separations shorter than the edge of an octahedron. 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.