Compact Packings of the Plane with Three Sizes of Discs

A compact packing is a set of non-overlapping discs where all the holes between discs are curvilinear triangles. There is only one compact packing by discs of radius 1. There are exactly 9 values of r which allow a compact packing with discs of radius 1 and r. It has been proven that at most 11462 p...

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Bibliographic Details
Published inDiscrete Geometry for Computer Imagery Vol. 11414; pp. 420 - 431
Main Authors Fernique, Thomas, Hashemi, Amir, Sizova, Olga
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2019
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Compact packing
Disc packing
Tiling
Online AccessGet full text
ISBN3030140849
9783030140847
ISSN0302-9743
1611-3349
DOI10.1007/978-3-030-14085-4_33

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Summary:A compact packing is a set of non-overlapping discs where all the holes between discs are curvilinear triangles. There is only one compact packing by discs of radius 1. There are exactly 9 values of r which allow a compact packing with discs of radius 1 and r. It has been proven that at most 11462 pairs (r, s) allow a compact packing with discs of radius 1, r and s. We prove that there are exactly 164 such pairs.
Bibliography:The work of O. S was supported within frameworks of the state task for ICP RAS 0082-2014-0001 (state registration AAAA-A17-117040610310-6). The work of Th. F and A. H was supported by the Partenariat Hubert Curien (PHC) Gundishapur.
ISBN:3030140849
9783030140847
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-14085-4_33