respectively. These mapping operators are defined so that the CG coordinates have welldefined physical definitions in terms of the FG coordinates. In the derivation of the MS-CG method for isotropic CG particles, it was shown that consistency between FG and CG models in momentum space requires that no FG particle contribute to more than one CG particle. Thus, we impose the same condition and, more specifically, represent the position and orientation of each CG particle as the center-of mass and principal axes of inertia of the group of FG particles that are mapped onto it. We define N non-intersecting subsets,