Welcome to the EPINET project

The EPINET project explores 2D hyperbolic (H²) tilings as a source of crystalline frameworks (or networks) in 3D euclidean (E³) space. Our aim is to enumerate networks with a broad spectrum of properties that are of possible interest to geometers, structural chemists, and statistical physicists. The guiding principal is one of hyperbolic surface tiling, where the 3D crystallinity of an underlying surface induces 3–periodic networks. The extraordinary wealth of hyperbolic tilings allows us to enumerate networks and their spatial realisations (“embeddings”) with greater breadth than conventional approaches.

Search the databases

• Hyperbolic Subgroup Tilings
• U-Tilings
• Hyperbolic Nets
• Systre Nets

Explore the databases

• Structure Taxonomy

Site Information

• About
• Changelog
• Contacts
• Acknowledgements
• Future Changes

Background Information

• Reference Pages that give an overview of the following topics:
• Minimal surfaces
• Covering maps
• Orbifolds
• Combinatorial tiling theory
• Hyperbolic Tiling
• Surface Reticulations
• Glossary
• Bibliography and recommended reading

• The following paper is the main reference for the techniques we use to generate the tilings and nets in the EPINET database. It is available from the Acta Crystallographica website.

  S.J. Ramsden, V. Robins and S.T. Hyde, “Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examples”, Acta Cryst. A 65, 81–108, (2009).