A Note on Using the Knowledge of Symmetry in the Rearrangement of Decorative Tile Patterns in Historical Buildings

In the past, the art of designing and painting tiles was passed from master to apprentice, and each time the creativity of different artists gave a different effect to these works. Therefore, the methods of drawing these motifs have never been written down. As we know, most of the motifs used in the decoration of historical tiles have a geometric origin, and their analysis or drawing requires knowledge of projection. Therefore, in this note, an attempt has been made to propose the hypothesis of the matching of symmetrical elements in the patterns of historical tiles with the symmetrical elements of material crystals, while examining the geometric structure of different motifs, rules based on symmetry data are presented for drawing these motifs. It is believed that with the help of this method, the rearrangement of traditional motifs in the tile production industry, as well as their recovery for the restoration of damaged parts using formula writing and marking, will become easier.