Some novel three-dimensional Euclidean crystalline networks derived from two-dimensional hyperbolic tilings
We demonstrate the usefulness of two-dimensional hyperbolic geometry as a tool to generate three-dimensional Euclidean (E3) networks. The technique involves projection of edges of tilings of the hyperbolic plane (H2) onto three-periodic, minimal surfaces, embedded in E 3. Given the extraordinary wealth of symmetries commensurate with H2, we can generate networks in E3 that are difficult to construct otherwise. In particular, we form four-, five- and seven-connected (E3) nets containing three-...[Show more]
|Collections||ANU Research Publications|
|Source:||European Physical Journal B|
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