List of planar symmetry groups

Planar symmetry groups refer to the mathematical groups that describe the symmetries present in two-dimensional shapes. These groups capture how a pattern can be transformed through rotations, translations, reflections, and glide reflections while preserving its overall structure. The main types of planar symmetry groups can be categorized into: 1. **Cyclic Groups (C_n)**: These consist of rotations about a point. For example, C_3 corresponds to a triangle where you can rotate the shape 120 degrees.