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12-Neighbour Packings of Unit Balls in \({\mathbb{E}^3}\)

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Abstract

We prove that any 12-neighbour packing of unit balls in \({\mathbb{E}^3}\) is composed of parallel layers of the same hexagonal structure as the layers in the densest lattice packing.

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Authors and Affiliations

  1. Department of Geometry, Eötvös Loránd University, 1117, Budapest, Pázmány Péter sétány 1/c, Hungary

    K. Böröczky

  2. Institute of Informatics and Economics, University of West-Hungary, 9400, Sopron, Bajcsy-Zsilinszky utca 9, Hungary

    L. Szabó

Authors
  1. K. Böröczky
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  2. L. Szabó
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Correspondence to L. Szabó.

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Böröczky, K., Szabó, L. 12-Neighbour Packings of Unit Balls in \({\mathbb{E}^3}\) . Acta Math. Hungar. 146, 421–448 (2015). https://doi.org/10.1007/s10474-015-0527-4

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  • DOI: https://doi.org/10.1007/s10474-015-0527-4

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