Pascal's Triangle and Its Relatives

Exercises

Symmetries of regular polygons

3. Here is an example using a pentagonal template.

Refelct across a vertical line, rotate 72 deg = 360/5 deg ccw, then reflect again across a vertical line. Note this is equivalent to a rotation by 72 deg cw.

The hexagonal template example is similar.

From bab = a^-1 we see (ab)² = (ab)(ab) = a(bab) = a(a^-1) = 1.

Return to Symmetries of Regular Polygons Exercises.