Hypothetical zeolite

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.

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.

The method of Earl et al.[1] uses simulated annealing to arrange a fixed number of tetrahedral atoms under periodic symmetry constraints.

This is then followed by a simulated annealing embedding of the candidate graph into the 3-dimensional torus.

Ockwig et al.[3] tile polyhedra to fill space and generate four-valent graphs.