2016/07/28 by Stäger, D. V., Herrmann, H. J.
#FOS: Mathematics #FOS: Physical sciences #Metric Geometry (math.MG) #Other Condensed Matter (cond-mat.other)
paper · doi:10.48550/arxiv.1607.08391
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.