運用二維對稱特性建構雙瓦片鋪磚之研究

Abstract

Brian Wichmann (Surrey, UK)與John Dawes (Berkshire, UK)首先提出雙瓦片鋪磚的概念[13]，以等面鋪磚(isohedral tiling)93種規格中53種為基準，發展出一套雙瓦片鋪磚法，同時發現雙瓦片鋪磚共有147種規格。對一般人而言，繪製這類的圖樣有很大的障礙，必須在特殊軟體上方可有效進行。因此，本研究主要目的希望研究出一套簡易的方式，讓雙瓦片的構圖能夠在一般的平台上可以完成。本研究發展出一套新的雙瓦片鋪磚法，直接採用10種二維對稱構圖，完成雙瓦片鋪磚。最後我們將這套方法實踐在數學簡報系統(Mathematical Presentation System, MathPS)上；該系統提供以結構複製法(Structural Cloning Method, SCM)為核心的構圖環境，可繪製複雜結構。

Wichmann and Dawes developed 147 kinds of the tiling of two prototiles using 53 isohedral tiling out of 93 specifications. It is complicated to draw those tiling via general graphic software. The purpose of this study is to develop a simple method and interface based on 10 two-dimension symmetrical patterns to draw two prototiles tiling. As the result, 147 two protitiles tiling could be constructed based on 16 similar dissections.