## Elementary Geometry for College Students (7th Edition)

If $n$ is the number of vertices of a regular polygon, the number of diagonals is: $\frac{n(n-3)}{2}$ If a regular polygon has 6 vertices, the number of diagonals is: $\frac{n(n-3)}{2} = \frac{6(6-3)}{2} = 9$ If a regular polygon has 7 vertices, the number of diagonals is: $\frac{n(n-3)}{2} = \frac{7(7-3)}{2} = 14$ If the number of vertices is less than 6, the number of diagonals is less than 9. If the number of vertices is more than 7, the number of diagonals is more than 14. Therefore, there is no regular polygon with 12 diagonals.