Feldspars, paracelsian and danburite, harmotome and phillipsite have alumino-silicate frameworks that consist of three out of the seventeen simplest ways of cross-linking chains of the feldspar type. The four-membered rings that form the feldspar type of chain are parallel and have two adjacent tetrahedra pointing one way and the other two the other way. Chains are produced by sharing oxygen atoms of oppositely-pointing tetrahedra of parallel four-membered rings. Cross-linking of chains produces frameworks containing parallel eight-membered rings. If alternate tetrahedra in the rings point the same way, a new type of chain is produced, and there are four simple ways of joining these chains together to make a framework. If all four tetrahedra in a ring point the same way, only one structure can be developed, which has been proposed already by Barrer et al. for the zeolite Na-P1 and other members of the harmotome family. If three tetrahedra in the ring point the same way, very many simple structures can be constructed, and the seven simplest of these are described. It is suggested from comparison of cell dimensions that gismondine and, perhaps, yugawaralite may belong to this series of hypotheti- cal structures. It is also suggested that some of the complexity and confusion in the harmotome group of zeolites may arise from hitherto unrecognized members of this hypothetical group. Major angular distortions from the ideal shape occur for the naturally-occurring silicates belonging to these structural groups.