A Mathematical Analysis of ZeolitesPublic
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Zeolites are naturally occurring minerals consisting of simple building blocks which mathematically correspond to tetrahedra. As a purely combinatorial concept, n-dimensional zeolites may be defined as line graphs of (n + 1)-regular graphs. Not all combinatorial zeolites have geometric realizations. We introduce the layer construction to obtain an (n + 1) dimensional geometric zeolite from an n-dimensional one. By interpreting the Harborth graph as a finite 2-dimensional geometric zeolite, we obtain, using the layer construction, a fi nite 3-dimensional geometric zeolite, which might be synthesized.
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