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

@article{Hyde2003SomeNT,
  title={Some novel three-dimensional Euclidean crystalline networks derived from two-dimensional hyperbolic tilings},
  author={Stephen T. Hyde and Stuart Ramsden},
  journal={The European Physical Journal B - Condensed Matter and Complex Systems},
  year={2003},
  volume={31},
  pages={273-284}
}
  • S. Hyde, S. Ramsden
  • Published 2003
  • Computer Science
  • The European Physical Journal B - Condensed Matter and Complex Systems
Abstract: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 E3. 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… 

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