Hypothetical zeolites are combinatorial models of potential structures of the minerals known aszeolites. They are four-regularperiodic graphs, with vertices representing the tetrahedral atom (usually Si or Al) and the edges representing the bridging oxygen atoms. Alternatively, by ignoring the tetrahedral atoms, zeolites can be represented by a six-valent periodic graph of oxygen atoms, with each O-O edge defining an edge of a tetrahedron.

At present there are millions of hypothetical zeolite frameworks known. For any fixed number of vertices, these are a small fraction of possible 4-regular periodic graphs, because the geometric constraints imposed by the chemistry of zeolites rules out most possibilities.

There are several methods for enumerating zeolite frameworks. The method of Earl et al.^[1] uses simulated annealing to arrange a fixed number of tetrahedral atoms under periodic symmetry constraints. The method of Treacy and Rivin^[2] uses combinatorialenumeration to identify four-valent graphs under fixed symmetry and fixed number of tetrahedral atoms. This is then followed by asimulated annealingembedding of the candidate graph into the 3-dimensionaltorus. Ockwig et al.^[3] tilepolyhedra to fill space and generate four-valent graphs.

There many open questions, among them:

• Why there is such a large discrepancy between the number of hypothetical zeolites and the number of zeolite frameworks observed in nature?
• Can the pore structure of a hypothetical zeolite be predicted only from its periodic graph?^[4]

• Atlas of Prospective Zeolite Structures
• Zeolite Project as ASU/Temple