The analysis of crystallographic symmetry types in finite groups

Abstract

Undeniably, it is human nature to prefer objects which are considered beautiful. Most consider beautiful as perfection, hence they try to create objects which are perfectly balance in shape and patterns. This creates a whole different kind of art, the kind that requires an object to be symmetrical. This leads to the study of symmetrical objects and pattern. Even mathematicians and ethnomathematicians are very interested with the essence of symmetry. One of these studies were conducted on the Malay traditional triaxial weaving culture. The patterns derived from this technique are symmetrical and this allows for further research. In this paper, the 17 symmetry types in a plane, known as the wallpaper groups, are studied and discussed. The wallpaper groups will then be applied to the triaxial patterns of food cover in Malaysia.