Frieze group
= Frieze group
{wiki}
A <discrete subgroup> of <Euclidean isometries> is a frieze group when its <translation subgroup> is infinite cyclic and has finite index. Translations along a line alone give $\mathbb Z$; adding perpendicular mirrors gives the <infinite dihedral group>, while adding a mirror along the translation direction gives $\mathbb Z\times C_2$. These groups describe patterns periodic in one planar direction.