There are centers of 3-fold rotation at the upper tip of each flying fish's left wing and the left tip of its tail. This tessellation has both translational and rotational symmetry. It is interesting to see basic geometric ideas and drawing techniques which Escher did by creating tessellations. It is interesting to study his art of tessellations and compare his tessellation to geometric forms. Related to this topic is the work of the artist M.C. If you need a detailed description of that principles, push the button. There are basically 4 ways of how a diagram can be “mapped onto” itself, namely, by translation, rotation, reflection and glide reflection.We will discover in the following diagrams, how this design can be “mapped onto” itself, which is the fundamental idea of how tessellations work. To illustrate the principles behind a simple tessellation pattern, a tiling consisting of equilateral triangles of degree 6 at each vertex will be used as an example to illustrate these principles.

There are certain principles of tessellations. There are exactly three regular tessellations composed of regular polygons symmetrically tiling the plane. Tessellations however, do not need the use of regular polygons, below is an example. By definition, tilings require the use of regular polygons put together such that it completely covers the plane without overlapping or leaving gaps. There is a difference between a tiling and a tessellation. In other words a tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes (n dimensions) is called a tessellation. What are tessellations? It is an arrangement of closed shapes that completely cover the plane without overlapping or leaving gaps.

Rotation tessellation