Tessellation is a pattern followed to cover a surface.
In order to fully understand the meaning of the term tessellation , it is necessary, first of all, to discover its etymological origin. In this case, it comes from the Latin tesella , which can be translated as “tile”, and this in turn from the Greek word tessares , which is synonymous with “four”.
The concept of tessellation is not part of the dictionary of the Royal Spanish Academy ( RAE ). The term that does appear is tessellation , referring to that which is made up of tesserae . The tesserae , in turn, are the different fragments that are part of a mosaic (a work that is made up of different pieces or pieces).
What is tessellation
The pattern that is followed when covering a surface is called tessellation. Tessellation requires avoiding overlapping figures and ensuring that no white spaces are recorded in the coating.
To develop the tessellation, it is usual to make reproductions of one or more tesserae until the entire surface is covered. It is important to note that irregular, semi-regular or regular tessellations can be made.
Depending on its characteristics, tessellation can be classified in different ways.
Classification according to type
Irregular tessellations are made up of polygons that are not regular. Semiregular tessellations , for their part, have at least two regular polygons, while regular tessellations are developed with regular hexagons, squares or equilateral triangles (using a single type).
In addition to these three types of tessellations exposed, the existence of a fourth type should also be noted. We are referring to the so-called demirregular tessellations. Under this name are the tessellations that are semiregular and that are formed from what is the set of eight semiregular tessellations and three regular cut tessellations. Thus, a total of fourteen demiregular tessellations are shaped.
Examples of tessellation
There are examples of tessellations all over the world. The tessellation composed of a pentagon with four sides of identical measurement and a sum of the angles of 540º (two of 108º, two of 90º and one of 144º) is known as the Cairo tessellation .
Another popular type of tessellation is the Penrose tessellation , named after the British mathematician Roger Penrose . These tessellations are aperiodic (they do not have translational symmetry): two have rotational symmetry of order five and an axis of symmetry.
There are many artists who, throughout their careers, have opted for tessellation as a key piece for the development of their works. However, among the most significant is the Dutchman Maurits Cornelis Escher , known artistically as MC Escher . This became a reference at the time because it resorted to tessellation to combine it with the plane and create all kinds of shapes, such as animals of various kinds, including fish and birds.