The Mathematics behind the EPINET Project

The EPINET project contributes to the enumeration of periodic networks in three–dimensional euclidean space (E³). These networks are of interest to geometers, structural chemists, and statistical physicists.

The following images show the framework structure of sodalite, which can be embedded on the P surface as shown in the middle. The network forms a tiling of the P surface which unwraps in the hyperbolic plane to a tiling by hexagons.

Sodalite on P surface

This project draws on several areas of geometry and crystallography. The following pages give illustrated and non-technical explanations of the key concepts.

Mathematical background
Related Work
  • A brief summary of other approaches to enumerating 3-periodic networks, and a note on the history of the EPINET project.
  • Papers, suggested further reading and links to related websites are collected on the site bibliography.