Compact Packings of the Plane with Three Sizes of Discs

  • Thomas FerniqueEmail author
  • Amir Hashemi
  • Olga Sizova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)


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 (rs) allow a compact packing with discs of radius 1, r and s. We prove that there are exactly 164 such pairs.


Compact packing Disc packing Tiling 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Univ. Paris 13, CNRS, Sorbonne Paris Cité, UMR 7030VilletaneuseFrance
  2. 2.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran
  3. 3.Faculty of MathematicsHigher School of EconomicsMoscowRussia
  4. 4.Semenov Institute of Chemical PhysicsMoscowRussia

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