We present a detailed study of the structure of the polymer phase of AC(60) (A = K, Rb) using data obtained from high-resolution neutron powder diffraction. We are able to obtain stable Rietveld refinements of both structures with no constraints on any carbon atom. KC60 has lattice parameters a 9.952 Angstrom, b = 9.091 Angstrom, c = 14,372 Angstrom in space group Pnmn and RbC60 has a = 10.125 Angstrom, b = 9.086 Angstrom, c = 14.207 Angstrom and beta = 90.316' in space group I12/m1. We notice significant distortion throughout the ball from its original icosahedral symmetry. Coordinates of the atoms will allow more accurate theoretical calculation of the physical properties of these fullerides and might shed light on the differences among the cations and the dimensionality of their electronic properties.