Exact solution of the vibration problem for the carbon-60 molecule

Utilizing the icosahedral symmetry of the C₆₀ molecule by amalgamating two methods, we solve the vibrational eigenfrequency problem for carbon-60 to obtain exact algebraic expressions for the characteristic polynomials of the vibmtion. The inter-atomic interaction consists of four force constants, two for bond-stretching and two for angle-oscillation.