Self-similar space-filling sphere packings in three and four dimensions
  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. 
D. V. St\"ager and H. J. Herrmann
cond-mat.other math.MG