The geometry of Niggli reduction: SAUC – search of alternative unit cells

A database of lattices using the G⁶ representation of the Niggli-reduced cell as the search key provides a more robust and complete search than older techniques. Searching is implemented by finding the distance from the probe cell to other cells using a topological embedding of the Niggli reduction in G⁶, so that all cells representing similar lattices will be found. The embedding provides the first fully linear measure of distances between unit cells. Comparison of results with those from older cell-based search algorithms suggests significant value in the new approach.