Zeolites: Geometry and Combinatorics

We study the background associated with phenomena observed in zeolites using combinatorial and geometric techniques. We define combinatorial d-dimensional zeolites and show that not all combinatorial zeolites have a unit distance realization inR , and of those that have a unit distance realization, not all have non-overlapping unit-distance realizations. Only few classes of finite 2-d zeolites are known and a long standing conjecture of Harborth suggests that there is only one type of non-overlapping unit distance realizable finite 2-d zeolites. However, for all d ≥ 2, we prove that there are uncountably many distinct infinite non-overlapping unit distance realizable zeolites. Infinite 3-d zeolites are the objects of interest to Chemists and Physicists and have important industrial applications.