English

Five-neighbour packings of centrally symmetric convex discs

Metric Geometry 2018-07-06 v1

Abstract

In an old paper of the author the thinnest five-neighbour packing of translates of a convex disc (different from a parallelogram) was determined. The minimal density was 3/73/7, and was attained for a certain packing of triangles. In that paper it was announced that for centrally symmetric convex plates (different from a parallelogram) the analogous minimal density was 9/149/14, and was attained for a certain packing of affine regular hexagons, and a very sketchy idea of the proof was given. In this paper we give details of this proof.

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Cite

@article{arxiv.1807.01907,
  title  = {Five-neighbour packings of centrally symmetric convex discs},
  author = {Endre Makai},
  journal= {arXiv preprint arXiv:1807.01907},
  year   = {2018}
}

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8 pages