Abstract
Inversive geometry can be used to generate exactly self-similar
space-filling sphere packings. We present a construction in two
dimensions and generalize this construction to search for packings in
higher dimensions. We discover 29 new three-dimensional topologies of
which 10 are bearings, and 13 new four-dimensional topologies of which
five are bearings. To characterize the packing topologies, we estimate
numerically their fractal dimensions and we analyze their contact
networks.
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