Tittel: The 17 Wallpaper Groups
Veileder: Markus Szymik
Sammendrag: Wallpaper groups, wallpaper patterns, planar patterns or plane repeating patterns. All different names for the same thing. A pattern that repeats itself infinitely, and can be found on e.g. wallpapers, tiling, textiles, potteries, ceramics, and in brick patterns. This text will explain what a wallpaper group is, how they are classified and to show that there are exactly 17 distinct patterns. This will be done by combining a traditional explanation of features that occur when discussing wallpaper groups together with a more colorful language used by John H. Conway in «The Symmetry of Things». The first proof for 17 groups was done by Evgraf Fedorov in 1891, however for this text, the proof will follow Conway’s ”Magic Theorem”.