Symmetry: A guide to its application in 2D electron crystallography

A defining property of a crystal is its symmetry. This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It begins by defining molecular point symmetries, before covering crystallographic symmetry operations in 2D, common notation, a summary of crystallographic plane groups and theoretical methods and important considerations for the identification and application of symmetry in 2D crystal images for 3D structure determination. While many of the concepts covered here may be equally applicable to point symmetry and space group symmetry in 3D, this review has been written from the perspective of 2D electron crystallography and deals specifically with symmetry operations and crystallographic space groups in 2D crystal projection images.