  Inversive geometry can be used to generate exactly self-similar space-filling
sphere packings. We present a construction method in two dimensions and
generalize it to search for packings in higher dimensions. We newly discover 29
three-dimensional and 13 four-dimensional topologies of which 10 and 5,
respectively, are bearings. To distinguish and characterize the packing
topologies, we numerically estimate their fractal dimensions and we analyze
their contact networks.
