Five-neighbour packings of centrally symmetric convex discs

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 \(3/7\), and was attained for a certain packing of triangles. In that paper it was announced that for centrally symmetric convex p...

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Bibliographic Details
Published in:arXiv.org 2018-07
Main Author: Makai, Endre
Format: Article
Language:English
Subjects:
Density
Hexagons
Online Access:Get full text
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Summary: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 \(3/7\), 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 \(9/14\), 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.
ISSN:2331-8422