The geometry of Niggli reduction: BGAOL – embedding Niggli reduction and analysis of boundaries. Erratum

Ambiguities in the article by Andrews & Bernstein [J. Appl. Cryst. (2014), 47, 346–359] are clarified.

The geometry of Niggli reduction: BGAOL -embedding Niggli reduction and analysis of boundaries

An implicit embedding of the space of Niggli-reduced cells in a higher-dimensional space to facilitate calculation of distances between cells is described. This distance metric is used to create a program, BGAOL, for Bravais lattice determination. Results from BGAOL are compared with results from other metric based Bravais lattice determination algorithms. This embedding depends on understanding the boundary polytopes of the Niggli-reduced cone N in the six-dimensional space G⁶.

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.