Generation of Polyiamonds for p6 Tiling by the Reverse Search

  • Takashi Horiyama
  • Shogo Yamane
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)


Polyiamonds are the two dimensional shapes made by connecting n unit triangles, joined along their edges. In this paper, we propose algorithms to generate polyiamonds for p6 tiling, i.e., those covering the plane by 6-fold rotations around two rotation centers (60 degrees rotations around the origin and 120 degrees rotations around the terminus). Our algorithm is based on the techniques of the reverse search: (1) No trial and error, since we design rules to generate the next. (2) No need to store already generated polyiamonds. According to these good properties and the proposed rule specific to p6 tiling, we have succeeded to generate 137,535 polyiamonds for p6 tiling up to n = 25, which include 2,246 polyiamonds up to n = 16 obtained by the conventional method.


Equivalence Class Additional Rule Degree Rotation Rotation Center Family Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Takashi Horiyama
    • 1
  • Shogo Yamane
    • 1
  1. 1.Graduate School of Science and EngineeringSaitama UniversityJapan

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