A wallpaper is <a href="https://en.wikipedia.org/wiki/Invariant_(mathematics)" class="extiw" title="w:Invariant (mathematics)">invariant</a> under an infinite number of <a href="https://en.wikipedia.org/wiki/Translation_(geometry)" class="extiw" title="w:Translation (geometry)">translations</a>, members of a <a href="https://en.wikipedia.org/wiki/Group_(mathematics)" class="extiw" title="w:Group (mathematics)">group</a>, of which the <a href="https://en.wikipedia.org/wiki/Binary_operation" class="extiw" title="w:Binary operation">operation</a> denoted <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,{\text{by }}\circ \ }"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mtext>by </mtext></mrow><mo>∘<!-- ∘ --></mo><mtext> </mtext></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \,{\text{by }}\circ \ }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b703cc6a8f1d4bbd73c7b3db4b3aba032375b51" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:6.263ex; height:2.509ex;" alt="{\displaystyle \,{\text{by }}\circ \ }"></span> is the <a href="https://en.wikipedia.org/wiki/Function_composition" class="extiw" title="w:Function composition">function composition</a>. A classification of wallpapers is exposed on <a href="https://en.wikipedia.org/wiki/Wallpaper_group" class="extiw" title="w:Wallpaper group">“Wallpaper group”</a>, according to the group of <a href="https://en.wikipedia.org/wiki/Isometry" class="extiw" title="w:Isometry">isometries</a> under which a given wallpaper is invariant.
<a href="//commons.wikimedia.org/wiki/User:Arthur_Baelde" title="User:Arthur Baelde">Arthur Baelde</a>
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<span class="int-own-work" lang="en">Own work</span>