Geometriae Dedicata

, Volume 49, Issue 1, pp 39–70 | Cite as

Spiral hexagonal circle packings in the plane

  • Alan F. Beardon
  • Tomasz Dubejko
  • Kenneth Stephenson


We discuss an intriguing geometric algorithm which generates infinite spiral patterns of packed circles in the plane. Using Kleinian group and covering theory, we construct a complex parametrization of all such patterns and characterize those whose circles have mutually disjoint interiors. We prove that these ‘coherent’ spirals, along with the regular hexagonal packing, give all possible hexagonal circle packings in the plane. Several examples are illustrated.


Complex Parametrization Kleinian Group Circle Packing Spiral Pattern Geometric Algorithm 
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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Alan F. Beardon
    • 1
  • Tomasz Dubejko
    • 2
  • Kenneth Stephenson
    • 2
  1. 1.Dept. of Pure Math. and Math. StatisticsUniversity of CambridgeCambridgeEngland
  2. 2.Dept. of MathematicsUniversity of TennesseeKnoxvilleUSA

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