Editing Glide reflection (section)

== Space groups ==

Glide planes are noted in the [[Hermann–Mauguin notation]] by ''a'', ''b'' or ''c'', depending on which axis the glide is along. (The orientation of the plane is determined by the position of the symbol in the Hermann–Mauguin designation.) If the axis is not defined, then the glide plane may be noted by ''g''. When the glide plane is parallel to the screen, these planes may be indicated by a bent arrow in which the arrowhead indicates the direction of the glide. When the glide plane is perpendicular to the screen, these planes can be represented either by dashed lines when the glide is parallel to the plane of the screen or dotted lines when the glide is perpendicular to the plane of the screen. Additionally, a centered lattice can cause a glide plane to exist in two directions at the same time. This type of glide plane may be indicated by a bent arrow with an arrowhead on both sides when the glide plan is parallel to the plane of the screen or a dashed and double-dotted line when the glide plane is perpendicular to the plane of the screen. There is also the ''n'' glide, which is a glide along the half of a diagonal of a face, and the ''d'' glide, which is along a fourth of either a face or space diagonal of the [[unit cell]] . The latter is often called the diamond glide plane as it features in the diamond structure. The ''n'' glide plane may be indicated by diagonal arrow when it is parallel to the plane of the screen or a dashed-dotted line when the glide plane is perpendicular to the plane of the screen. A ''d'' glide plane may be indicated by a diagonal half-arrow if the glide plane is parallel to the plane of the screen or a dashed-dotted line with arrows if the glide plane is perpendicular to the plane of the screen. If a ''d'' glide plane is present in a crystal system, then that crystal must have a centered lattice.<ref>{{cite web |title=Glide Planes |url=http://img.chem.ucl.ac.uk/sgp/misc/glide.htm |website=Birkbeck College, University of London |accessdate=24 April 2019 |archive-date=21 July 2019 |archive-url=https://web.archive.org/web/20190721220633/http://img.chem.ucl.ac.uk/sgp/misc/glide.htm |url-status=live }}</ref>

In today's version of Hermann–Mauguin notation, the symbol ''e'' is used in cases where there are two possible ways of designating the glide direction because both are true. For example if a crystal has a base-centered [[Bravais lattice]] centered on the C face, then a glide of half a cell unit in the ''a'' direction gives the same result as a glide of half a cell unit in the ''b'' direction.

The [[isometry group]] generated by just a glide reflection is an infinite [[cyclic group]]. Combining two equal glide plane operations gives a pure translation with a translation vector that is twice that of the glide reflection, so the even powers of the glide reflection form a translation group.

In the case of glide-reflection symmetry, the [[symmetry group]] of an object contains a glide reflection and the group generated by it. For any symmetry group containing a glide reflection, the glide vector is one half of an element of the translation group. If the translation vector of a glide plane operation is itself an element of the translation group, then the corresponding glide plane symmetry reduces to a combination of [[reflection symmetry]] and [[translational symmetry]].