Isometries of the Euclidean plane fall into four categories (see the article Euclidean plane isometry for more information).
*Translations, denoted by T, where v is a vector in R. This has the effect of shifting the plane applying displacement vector v.
*Rotations, denoted by R, where c is a point in the plane (the centre of rotation), and θ is the angle of rotation.
*Reflections, or mirror isometries, denoted by F, where L is a line in R. (F is for "flip"). This has the effect of reflecting the plane in the line L, called the reflection axis or the associated mirror.
*Glide reflections, denoted by G, where L is a line in R and d is a distance. This is a combination of a reflection in the line L and a translation along L by a distance d.