Symmetries of a Regular Polygon
Symmetries of a Regular Polygon
Here we explore the symmetries of a regular polygon. Checking the Summary checkbox gives the general result for the identity, n-1 rotations, and n reflections comprising the symmetry group. For n = 3, 4, and 5 an operation table for the group can be displayed. For n = 3 and 4 the elements are given as symmetries, in terms of the generating rotation and reflection and in cycle notation. Perform the isometry on the column on the left first and then the one on the row at the top next. The cycle (1 2 3) indicates that the image of vertex 1 is vertex 2, the image of vertex 2 is vertex 3, and the image of vertex 3 is vertex 1. 1 indicates the identity transformation.