A frieze is a two-dimensional design that repeats in one direction.
Such patterns occur frequently in architecture and decorative art.
Frieze patterns can be classified into seven types according to their symmetries.
see also the 4 basic Symmetries
they are part of the bigger 17 wallpaper groups
p1 / p1
Translation
p2 / p2
Translation +
180° Rotations
pg
Glide-reflections + Translations
pm
Translation+
Mirror Reflection
in the vertical axis.
p2mm / pmm
(TRHVG) Horizontal and Vertical reflection lines, Translations and 180° Rotations:
This group requires three generators, with one generating set consisting of a translation, the reflection in the horizontal axis and a reflection across a vertical axis.
p2mg / cm
(TRVG) Vertical reflection lines, Glide reflections, Translations and 180° Rotations:
The translations here arise from the glide reflections, so this group is generated by a glide reflection and either a rotation or a vertical reflection.
p11m / pmg
(THG) Translations, Horizontal reflections, Glide reflections:
This group is generated by a translation and the reflection in the horizontal axis. The glide reflection here arises as the composition of translation and horizontal reflection
try them for yourself painting on this webpage
