The only regular polygons that can be constructed with a straightedge and
compass are those for where the number of sides is a product of a
power of 2 and of primes of the form \(\displaystyle 2^{2^{n}} + 1\). For example,
a regular polygon with 30 sides can be constructed because 30 is
2*3*5, and 3 is 2 + 1 or \(\displaystyle 2^{2^{0}}\) + 1 and 5 is \(\displaystyle 2^{2} + 1\) or \(\displaystyle 2^{2^{1}}\) + 1. But
9 is 3 * 3, and while 3 is a prime of the right form, the fact that
you have 2 factors of 3 means it won't work. Gauss was the first to
construct a regular polygon with 17 sides, which you can see is
possible because \(\displaystyle 17=2^{2^{2}} + 1\).
I, myself, have not constructed a 17-gon with a straight edge and compass.
Good luck. It's possible, but how difficult I do not know.
