Plane symmetry

• Reflection groups. These are plane symmetry groups that are generated by reflections, possibly limited to reflections in lines through the origin.
• Rotation groups. These groups consist of rotations around a point.
• Translation groups.
• Symmetries of geometrical figures. Some of these are reflection groups, e.g., the group of symmetries of the square or the rectangle. The symmetry group of a swastika or any similar figure without an axis of symmetry is a rotation group.