Retrieving "Two Dimensional Crystallographic Groups" from the archives

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1. Wallpaper Groups

   Linked via "two-dimensional crystallographic groups"

   Wallpaper groups, also known as two-dimensional crystallographic groups, constitute the set of all possible isometry groups of the Euclidean plane ($\mathbb{E}^2$) that possess a discrete subgroup of translations $T$ such that the quotient space $\mathbb{E}^2/T$ is compact. These groups are fundamental in describing the symmetry inherent in patterns that repeat infinitely in two dimensions, such as those found in tiling, textile design…