A simple and efficient method is presented for the enumeration of substitution isomers for polyhedral molecules with face spirals. For these molecules, it is convenient to find a set of symmetry-equivalent vertex sequences, each corresponding to a symmetry operation of the point group of the parent framework. This enables us to represent each symmetry operation as permutation of vertices, with which the isomorphic configurations and the symmetry of a substitution isomer are readily found, thus solving the enumeration problem. The method is applied to the fullerene-24 cage and the truncated octahedron for enumerating the related B24-mNm isomers and for assigning their maximal symmetry. A discussion on the symmetry of these isomers is also presented.