Plane Group Symmetry Elements (Two Dimensions) 

The symmetry elements which form the basis of the 17 plane groups are the 2, 3, 4, and 6fold rotations plus the mirror and glide. 

2Fold Rotation Axes 


The rotation axis is perpendicular to the page. A twofold rotation consists of rotation by 360/2 = 180 degrees. Thus these hands are related by a twofold axis of rotation. 
3Fold Rotation Axes 


The rotation axis is perpendicular to the page. A threefold rotation consists of rotation by 360/3 = 120 degrees. Thus these hands are related by a threefold axis. 
4Fold Rotation Axes 


The rotation axis is perpendicular to the page. A fourfold rotation consists of rotation by 360/4 = 90 degrees. Thus these hands are related by a fourfold axis.

6Fold Rotation Axes 


The rotation axis is perpendicular to the page. A sixfold rotation consists of rotation by 360/6 = 60 degrees. Thus these hands are related by a sixfold axis.

Reflection Planes: Mirrors 

The reflection plane is perpendicular to the page. These two hands are mirror images. Thus they are related by a reflection plane.


Reflection Plane: Glides 


The glide plane is perpendicular to the page. A glide consists of a reflection followed by a translation.

