A general-method for the computer-assisted generation of polyhedra-based cluster structures is introduced. The cluster family of interest is delimited, and its definitive structural elements are employed in the design of an infinitely extended parent solid. For computational facility, this polyhedra-based solid is transformed into a parallel graph representation consisting of a simple lattice of points and lines. In connection with the structure-graph relationship, a descriptive notation detailing the local connectivity of constituent polyhedra is developed for use with both clusters and solids. Pieces of the lattice, corresponding to fragments of the parent solid, are generated by a straightforward recursive procedure. These fragments are converted into ligated clusters, and their structures are compiled in a database. Database structures are then subjected to four types of cluster rearrangement processes (folding, fusion, closure, and condensation) defined herein. Any relevant new structures which result are added to the database. The database is arranged by chemical formulae, and clusters of particular interest are sorted from it by whatever criteria are deemed. appropriate. With the aid of electronic energy calculations, relative stabilities of structural isomers may then be evaluated, leading to some measure of predictive capability. The primary advantage of this approach lies in its ability to produce immediately accessible structures with tailored stereochemistries. The entire procedure is demonstrated for edge-sharing tetrahedra-based structures typical of the iron-sulfur/selenium cluster family. These structures, derived from a parent solid with the antifluorite structure, are enumerated for formulae containing eight or fewer tetrahedral metal centers. Attention is focused on clusters with chalcogenide bridging modalities of four or less, and containing one or fewer associated terminal ligands per metal atom. Relative energies of selected [FemSqCll](n-) isomers with m < 7 are calculated via the extended Huckel method, and on the basis of these results, structures are proposed for some possible synthetic targets. Applications involving cluster synthesis, structural models employed during the crystallographic resolution of cluster-containing biomolecules, and elucidation of laser ablated cluster ions are briefly discussed.