As a basis for the rotational alignments, we first generate a set of points that fill and thus characterize the cavity of each cage. We successively insert helium adsorbates at random positions within a sphere circumscribing the cage molecule, rejecting the positions that overlap atoms of the cage and keeping the positions that were classified as void space; this set of points constitutes the porosity point cloud of a cage. We bias the insertions towards the center of the cage to emphasize the inner-cavity. See Sec. S2.1 for more details and We use the rotational dynamics of the porosity point cloud as a first attempt to align the cages on the basis of their cavity shapes. We rotated each cage so that the principal axes of rotation of its porosity point cloud are aligned with the x, y, and z Cartesian coordinate axes, with principal moments of inertia arranged in a non-increasing order. See Sec. S2.2. However, the cavity shapes of most cage molecules exhibit a degree of symmetry so as to render the computed principal axes of rotation sensitive to very small changes in the structure. i.e., the We employed Coherent Point Drift 51 to find the optimal rotation matrix to align the porosity point cloud of one cage, Y to the porosity point cloud of an another cage, X .