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Example pattern with this symmetry group: A typical example of glide reflection in everyday life would be the track of footprints left in the sand by a person walking on a beach. Frieze group nr. 6 (glide-reflections, translations and rotations) is generated by a glide reflection and a rotation about a point on the line of reflection.
The symbols are either m, g, or 1, for mirror, glide reflection, or none. The axis of the mirror or glide reflection is perpendicular to the main axis for the first letter, and either parallel or tilted 180°/n (when n > 2) for the second letter. Many groups include other symmetries implied by the given ones.
In the case of symmetry groups in the plane, additional parameters are the direction of the translation vector, and, for the frieze groups with horizontal line reflection, glide reflection, or 180° rotation (groups 3–7), the position of the reflection axis or rotation point in the direction perpendicular to the translation vector.
A reflection plane m within the point groups can be replaced by a glide plane, labeled as a, b, or c depending on which axis the glide is along. 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 quarter of either a face or space diagonal of the unit cell.
There are four types: translations, rotations, reflections, and glide reflections (see below § Classification). The set of Euclidean plane isometries forms a group under composition: the Euclidean group in two dimensions. It is generated by reflections in lines, and every element of the Euclidean group is the composite of at most three ...
This group is singly generated, by a glide reflection, with translations being obtained by combining two glide reflections. p1m1 [∞] C ∞v Dih ∞ *∞∞ sidle (TV) Vertical reflection lines and Translations: The group is the same as the non-trivial group in the one-dimensional case; it is generated by a translation and a reflection in the ...
Examples of such groups are, in 1D, the group generated by a translation of 1 and one ... Glide reflections with translation by the same distance are in the same class.
This group is singly generated, by a glide reflection, with translations being obtained by combining two glide reflections. p1m1 [∞] C ∞v Dih ∞ *∞∞ sidle (TV) Vertical reflection lines and Translations: The group is the same as the non-trivial group in the one-dimensional case; it is generated by a translation and a reflection in the ...