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Regular sphere packings

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Abstract.

A collection of non-overlapping spheres in the space is called a packing. Two spheres are said to be neighbours if they have a boundary point in common. A packing is called k-regular if each sphere has exactly k neighbours. We are concerned with the following question. What is the minimum number of not necessarily congruent spheres which may form a k-regular packing? In general, for which natural numbers n and k does there exist a connected k-regular packing of exactly n spheres?

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Authors and Affiliations

  1. Diskrete Mathematik, Technische Universität Braunschweig, D-38023 Braunschweig, Germany, , , , , , DE

    H. Harborth

  2. Computer and Automation Research Institute, Hungarian Academy of Sciences, Lágymányosi u. 11, H-1111 Budapest, Hungary, , , , , , HU

    L. Szabó

  3. Department of Geometry, Eötvös University, Kecskeméti utca 10-12, H-1053 Budapest, Hungary, , , , , , HU

    Z. Ujváry-Menyhárt

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  1. H. Harborth
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  2. L. Szabó
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  3. Z. Ujváry-Menyhárt
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Eingegangen am 20. 3. 2000

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Harborth, H., Szabó, L. & Ujváry-Menyhárt, Z. Regular sphere packings. Arch. Math. 78, 81–89 (2002). https://doi.org/10.1007/s00013-002-8219-z

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  • DOI: https://doi.org/10.1007/s00013-002-8219-z

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