Embedment of symmetry groups in the triaxial patterns of food covers in Malaysia

Abstract

Triaxial weaving technique is a fading historical heritage in Malaysia. Besides Malaysia, this technique can be found in countries across the world such as Africa and South America. In Malaysia, this technique is used to produce the Malay traditional food covers through an intricate process in the form of a conic shape. Along the process, the triaxial weaving technique used by the food cover weavers produces beautiful symmetrical patterns. The symmetrical properties of the triaxial patterns including the food cover patterns have intrigued many mathematicians especially ethnomathematicians. In this research, the symmetrical properties possessed by the food cover patterns are found to be similar to the symmetrical properties found in crystals. Therefore, it justifies the implementation of the crystallographic symmetric types, also known as the wallpaper groups, on these patterns. The patterns were then analysed based on their groups and therefore, the generalised properties of these patterns were listed according to the concepts in group theory. Additionally, a new approach was developed to imitate the process of framework making which is an essential part of the food cover weaving. Through this method, more patterns were able to be introduced in this research. Finally, some of those patterns were also analysed and categorised into wallpaper groups.