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 a broad spectrum of networks 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.

Start exploring the EPINET site:

2D Hyperbolic Tilings

• The 2D Tilings Index is a listing of all the hyperbolic tilings.
• The PGD Kaleidoscopic Subgroups Index is a listing of the hyperbolic tilings organised by their H² symmetry subgroup.
• The 2D search page enables queries on topological properties or symmetry orbifold of hyperbolic tilings.

3D Periodic Networks

• The 3D Networks Index is a listing of the topologically distinct 3D euclidean networks generated by wrapping the 2D hyperbolic tilings onto appropriate periodic minimal surfaces.
• The Spacegroups Index is a listing of the 3D networks organised by their maximum symmetry E³ crystallographic spacegroup.
• The 3D search page enables queries on topological properties of the networks and the crystallographic classes of their maximum symmetry spacegroups.
• Crystallographers and chemists may be interested in some well–known examples of 3D networks that have been collected in the Known 3D Networks Index.

Tilings by infinite tiles

On the Infinite tile page we present preliminary examples of hyperbolic tilings by infinite tiles and their resulting multi-component embeddings in 3D (rod packings and interpenetrating networks).

Learn More About The EPINET Project:

What's New?

Keep up to date with the latest changes, additions and fixes to the EPINET site on the What's New? page.

About EPINET

The About EPINET page is a descriptive index into a wealth of expository material about the tools and techniques we use.

Glossary

The technical terms used throughout the site are summarised in the EPINET Project Glossary.

Contacts

Like to contact the project group or learn more about the people behind the EPINET project? Take a look at the EPINET Contacts page.