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Any space-filling packing of spheres can be cut by a plane to obtain aspace-filling packing of disks. Here, we deal with space-filling packingsgenerated using inversive geometry leading to exactly self-similar fractalpackings. First, we prove that cutting along a random hyperplane leads ingeneral to a packing with a fractal dimension of the one of the uncut packingminus one. Second, we find special cuts which can be constructed themselves byinversive geometry. Such special cuts have specific fractal dimensions, whichwe demonstrate by cutting a three- and a four-dimensional packing. The increasein the number of found special cuts with respect to a cutoff parameter suggeststhe existence of infinitely many topologies with distinct fractal dimensions.

Cutting self-similar space-filling sphere packings