Impresión de diseños simétricos en la obra de Escher

Abstract

In his need to find beautiful designs, forms and colors in the decoration of walls and the tiling of floors, humankind produced symmetric patterns that are examples of the concept of tessellation. In its own way, in order to solve its problems, nature had found wonderful tessellations. A tessellation or a surface tilling is the process of covering completely a surface with one type of tile that is repeated over and over without gaps or overlaps. Although it seems that there are infinitely many ways to produce symmetric plane designs, there are basically only 17 possible ways to produce a design. We will show that the execution of these tessellations follows some simple and concise rules, that we have used to construct 17 artifacts that can be used in the impression of any symmetric plane design. These artifacts are practical examples of Bill Thurston´s concept of Orbifold. As an illustration of our presentation, we will exhibit these artifacts by using some pictures and some of Escher´s designs. We will show that it is possible to teach, in an easy way, the concepts of rotation, translation and reflection by using these artifacts.