Generation of polyiamonds for p6 tiling by the reverse search

Authors:
Takashi Horiyama;Shogo Yamane
Affiliations:
Graduate School of Science and Engineering, Saitama University, Saitama, Japan;Graduate School of Science and Engineering, Saitama University, Saitama, Japan
Venue:
CGGA'10 Proceedings of the 9th international conference on Computational Geometry, Graphs and Applications
Year:
2010

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Abstract

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.