Pascal's Triangle and Its Relatives

Exercises

Symmetries of regular polygons

1. If the number of sides is odd, there is a reflection across the perpendicular bisector of each side, so n reflections.

If the number of sides is even, the perpendicular bisector of each side is also the perpendicular bisector of the opposite side, so there are only n/2 reflections across perpendicular bisectors of sides.

But there are also reflections across the bisectors of each vertex. The bisector of each vertex also bisects the opposite vertex, so these account for n/2 reflections.

(If n is odd, the perpendicular bisector of each side also bisects the opposite vertex.)

Return to Symmetries of Regular Polygons Exercises.