Editing Glide reflection (section)

== Wallpaper groups ==
Glide-reflection symmetry with respect to two parallel lines with the same translation implies that there is also translational symmetry in the direction perpendicular to these lines, with a translation distance which is twice the distance between glide reflection lines. This corresponds to [[wallpaper group]] pg; with additional symmetry it occurs also in pmg, pgg and p4g.

If there are also true reflection lines in the same direction then they are evenly spaced between the glide reflection lines. A glide reflection line parallel to a true reflection line already implies this situation. This corresponds to wallpaper group cm. The translational symmetry is given by oblique translation vectors from one point on a true reflection line to two points on the next, supporting a [[rhombus]] with the true reflection line as one of the diagonals. With additional symmetry it occurs also in cmm, p3m1, p31m, p4m and p6m.

In the [[Euclidean plane]] 3 of 17 [[wallpaper group]]s require glide reflection generators. p2gg has orthogonal glide reflections and 2-fold rotations. cm has parallel mirrors and glides, and pg has parallel glides. (Glide reflections are shown below as dashed lines)
{| class=wikitable style="text-align: center
|+ Wallpaper group lattice domains, and fundamental domains (yellow)
|-
! Crystallographic name
| pgg
| cm
| pg
|-
! Conway name
| 22×
| *×
| ××
|-
! Diagram
|[[File:Wallpaper group diagram pgg.svg|240px]]
|[[File:Wallpaper group diagram cm rotated.svg|240px]]
|[[File:Wallpaper group diagram pg.svg|240px]]
|-
! Example
|[[File:SymBlend pgg.svg|240px]]
|[[File:SymBlend cm.svg|240px]]
|[[File:SymBlend pg.svg|240px]]
|}