= Frieze group
{wiki}
A frieze <group> is a <discrete subgroup> of the <isometry group> of the <Euclidean plane> whose <translation subgroup> is infinite cyclic and has finite index. It describes a pattern periodic in one planar direction. The planar hypothesis is part of the definition; analogous <groups> acting in three-dimensional <Euclidean space> need not be frieze <groups>.
Translations along a fixed <line> give $\mathbb Z$. Adding reflections in perpendicular parallel <lines> gives the <infinite dihedral group>; adding a reflection in the translation axis instead gives $\mathbb Z\times C_2$. A <glide reflection> supplies another way to combine the single periodic direction with orientation reversal.
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