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Some novel three-dimensional Euclidean crystalline networks derived from two-dimensional hyperbolic tilings

Hyde, Stephen; Ramsden, Stuart


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]

CollectionsANU Research Publications
Date published: 2003
Type: Journal article
Source: European Physical Journal B
DOI: 10.1140/epjb/e2003-00032-8


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