Back Grŵp papur wal Welsh Tapetgruppe Danish Ebene kristallographische Gruppe German Grupo del papel pintado Spanish Groupe de papier peint French Grup kertas dinding ID 文様群 Japanese 평면의 결정군 Korean Behangpatroongroep Dutch Группа орнамента Russian
A wallpaper is a mathematical object covering a whole Euclidean plane by repeating a motif indefinitely, in manner that certain isometries keep the drawing unchanged. For each wallpaper there corresponds a group of congruent transformations, with function composition as the group operation. Thus, a wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two‑dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, especially in textiles, tessellations, tiles and physical wallpaper.