Symmetric Tiling Patterns with the Extended Picard Group in Three-Dimensional Space

  • Rui-song Ye
  • Jian Ma
  • Hui-liang Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4035)


Automatic generation of tiling patterns with the symmetry of the extended Picard group in three-dimensional hyperbolic space is considered. We generate the patterns by repeating the fundamental patterns created in the fundamental region to all other equivalent regions. We also produce such a kind of tiling patterns in the unit sphere by conformal mappings. The method provides a novel approach for devising exotic symmetric tiling patterns from a dynamical system’s point of view.


Conformal Mapping Hyperbolic Space Modular Group Symmetric Pattern Fundamental Region 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rui-song Ye
    • 1
  • Jian Ma
    • 1
  • Hui-liang Li
    • 1
  1. 1.Department of MathematicsShantou UniversityShantou, GuangdongP.R. China

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