Thesis advisor: Mark Reeder / A polynomial is said to be invariant for a group of linear fractional transformations G if its roots are permuted by G. We begin by using a simple group of linear fractional transformations that is isomorphic to S_{3} and finding its invariant polynomials to build up the tools necessary to attack a larger group. We then follow a construction from Toth of the icosahedral group I, and derive a general formula for all polynomials of degree 60 that are invariant under I. / Thesis (BA) — Boston College, 2004. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Mathematics. / Discipline: College Honors Program.