abstract: Zeolites are a class of microporous materials that are immensely useful as molecular sieves and catalysts. While there exist millions of hypothetical zeolite topologies, only 206 have been recognized to exist in nature, and the question remains: What distinguishes known zeolite topologies from their hypothetical counterparts? It has been found that all 206 of the known zeolites can be represented as networks of rigid perfect tetrahedra that hinge freely at the connected corners. The range of configurations over which the corresponding geometric constraints can be met has been termed the "flexibility window". Only a small percentage of hypothetical types exhibit a flexibility window, and it is thus proposed that this simple geometric property, the existence of a flexibility window, provides a reliable benchmark for distinguishing potentially realizable hypothetical structures from their infeasible counterparts. As a first approximation of the behavior of real zeolite materials, the flexibility window provides additional useful insights into structure and composition. In this thesis, various methods for locating and exploring the flexibility window are discussed. Also examined is the assumption that the tetrahedral corners are force-free. This is a reasonable approximation in silicates for Si-O-Si angles above ~135°. However, the approximation is poor for germanates, where Ge-O-Ge angles are constrained to the range ~120°-145°. Lastly, a class of interesting low-density hypothetical zeolites is evaluated based on the feasibility criteria introduced. / Dissertation/Thesis / Ph.D. Physics 2013