Self-similar space-filling sphere packings in three and four dimensions

D. V. Stäger; H. J. Herrmann

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arXiv · 1607.08391

Self-similar space-filling sphere packings in three and four dimensions

D. V. Stäger·H. J. Herrmann

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Abstract

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.

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D. V. Stäger, H. J. Herrmann. 2016-07-28. Self-similar space-filling sphere packings in three and four dimensions. https://arxiv.org/abs/1607.08391

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