the 4 basic symmetries

translate - rotate - reflect - glide

4 basic transformations to repeat and maintain symmetry along a strip:
Euclidean plane isometry is any way of transforming the plane without “deforming” it.

translation

rigid motion along the strip
the pattern slides

reflection

mirros across a line
horisontal
vertical

glide
reflection

reflect line
translate along strip

rotation

90 degree increments


source wikipedia