1083x1431 Traditional Wallpaper Patterns - Group ...

These groups are classified by the types of isometries (distance-preserving transformations) they contain:

: m for mirrors, g for glides, or 1 for no symmetry in that direction.

: A combination of a reflection and a translation along the mirror axis. Understanding the Notation (IUC) 1083x1431 Traditional Wallpaper Patterns Group ...

: Every wallpaper group must have translations in two independent directions.

: The highest order of rotation (1, 2, 3, 4, or 6). These groups are classified by the types of

A "wallpaper group" is a mathematical classification system for two-dimensional repetitive patterns based on their symmetries. There are exactly that can tile a plane, a fact famously proven by Evgraf Fedorov and later George Pólya. The 17 Wallpaper Groups

The standard International Union of Crystallography (IUC) notation uses a four-symbol code to describe these patterns: : Starts with p (primitive) or c (centered). : The highest order of rotation (1, 2, 3, 4, or 6)

: Possible orders are 2, 3, 4, or 6 (180°, 120°, 90°, and 60°). Reflections : Mirror symmetry across an axis.