We then iteratively aligned each unaligned cage whose porosity point cloud possesses nearly degenerate principal axes of rotation with an aligned cage. Let A be the set of 18 cages aligned by the authority of the rotational dynamics of their porosity point clouds and U be the set of remaining 56 cages not yet aligned. We use Coherent Point Drift to find which cage u ∈ U aligns best (the largest likelihood) with a cage in A. We then align this cage u to the cage a ∈ A with which it aligns best. We then remove u from the set of unaligned cages U and add it to the set of aligned cages A and repeat this process until U is empty. See Tab. S2 for the directed graph of cage alignments.