Problem #WSP-000300

Problem

Let $n\ge 3$ be a positive integer. A regular $n$-gon is a polygon with $n$ sides where every side has the same length, and every angle is the same. For example, a regular $3$-gon is an equilateral triangle, and a regular $4$-gon is a square.

What symmetries does a regular $n$-gon have, and how many?