What is Affine symmetric group?
Flat, [[Polygon|straight-edged shapes]] (like [[Triangle|triangles]]) or [[Polyhedron|3D ones]] (like [[Pyramid (geometry)|pyramids]]) have only a finite number of [[Symmetry|symmetries]] - ways to reflect or rotate it where it looks the same. In contrast, the '''affine symmetric group''' is a way to [[Mathematics|mathematically]] describe all the symmetries possible when an [[Plane (mathematics)|infinitely large flat surface]] is covered by [[Tessellation|triangular tiles]]. As with many subjects in mathematics, it can also be thought of in a number ways: for example, it also describes the symmetries of the infinitely long [[number line]], or the possible arrangements of all [[integers|whole numbers]] (..., −2, −1, 0, 1, 2, ...) with certain [[Permutation|repetitive patterns]]. As a result, studying the affine symmetric group extends the study of symmetries of polyhedra or of groups of permutations to the [[Infinity|infinite case]]. It also connects several topics in mathematics that were originally studied for independent reasons, ranging from complex reflection groups to [[Juggling|juggling sequences]]. [[Category:Geometry]] [[Category:Symmetry]] [[Category:Abstract algebra]]