...
...
Translation is a shift in a given direction.
...
...
...
...
An infinitely repeating pattern has translation as a symmetry - the entire pattern can be shifted over without changing in appearance:
Mirror Reflection is a reflection across an imaginary line.
A pattern has mirror reflection as a symmetry if the entire pattern can reflect across a line yet remain unchanged:
Glide Reflection composes translation and mirror reflection: A glide reflection reflects across a mirror line at the same time as translating along it.
Infinitely repeating patterns can have glide reflections:
Rotation is a symmetry that turns a pattern around a point.
½ turn rotation:
¼ turn rotation:
⅓ turn rotation:
⅙ turn rotation:
These symmetries can be combined in patterns that repeat infinitely. Play with their combinations: http://beautifulsymmetry.onl/wallpaper.