Every polygon can be represented as a triangle.īecause each triangle has three sides, this kind of tessellation is referred to as a 3.3.3 tessellation (see Figure 1, though due to slight drawing errors, it’s not a regular tessellation). After that, we consider the number of polygons that converge at that vertex. First, we pick a vertex from within the pattern to work with. Example Problem on Tessellation PatternsĮxplain how a regular polygon can form a pattern that tessellates. After that, select the polygons that surround it based on the total number of facets that each one possesses. It makes no difference which vertex you choose to use. A vertex is a nook within a polygon, so keep in mind what this means. You will start by picking a vertex from within the pattern. Geometric shapes can be given names based on the machines that were used to create them. There are three different shapes that can be used to create regular tessellations: an evenly spaced triangle, a rectangular shape, or a hexagon. Consider the fact that all the angles and aspects of a regular polygon are the same. Classification of TessellationĪ structure that is created by repeatedly using a regular polygon is referred to as a normal tessellation. They are a component of a branch of mathematics that frequently gives the impression that it is simple to understand, but research shows that they are, in fact, quite hard. Tessellations are utilized extensively in regular things, particularly in the construction of walls and structures. One artist, MC Escher, who was from the Netherlands, is known for incorporating a lot of intricate tessellations into his work. Tessellations and the various ways that they can be employed in building design because of their malleability and potential application in the visual arts and built environment, tessellations are an essential component of the mathematical discipline of mathematics. Regular pentagons that are all the same can’t make tessellations on their own. This is also true of a pentagonal tessellation, in which pentagons can fit together, but only when they change size and shape. This is called an irregular tessellation. They might be components of a tessellation, and the spaces between them could be seen as a different kind of shape. A honeycomb is an example of an everyday object with a hexagonal tessellation pattern.Įvidently, some shapes, like circles, can’t tessellate because they don’t fit together perfectly. This happens because these shapes can fit together without any gaps, and they will all look the same in the pattern. These are squares, hexagons, and equilateral triangles. There are only three types of shapes that can make tessellation patterns by themselves. Only triangles, squares, and hexagons, which are the only shapes with equal sides and angles, can make a tessellation on their own. When two or even more polygons meet at a point in a tessellation, or when two or even more polygons meet at a certain vertex, the inner angles should add up to 360°. You can give a name to a tessellation by focusing on the vertex and noting the side of all the structures that converge at the vertex at the same time. The point where two shapes meet, also known as the corner point, is referred to as the vertex. It follows that there are only three distinct types of regular tessellations: those constructed from squares, equilateral triangles, and hexagons. They are used rather frequently in works of art, patterns for clothing, designs for pottery, and blown glass windows. These days, tessellations are employed for the floors, walls, and ceilings that are found inside buildings. In addition, the tessellations that are used in architecture may be seen at Fatehpur Sikri. The Alhambra Palace in Granada, which is in the southern region of Spain, is an example of a Muslim edifice that hints at the presence of tessellations. Tessellations, which are miniature quadrilaterals used in computer games and in the construction of mosaics, were exploited by the ancient Greeks. Tessellations had been tracked all the way back to the ancient civilizations, where they were first discovered (around 4000 BC). They frequently exhibit certain qualities that are tied to their place of origin in some way. There is evidence that tessellations were used in a variety of ancient cultures across the world. The word “tessellation” originates from the Latin verb tessellate, which translates to “to pave,” or the word “ tessella,” which refers to a little, rectangular stone. The only rule is that all of the sides must fit together perfectly, with no empty spaces or overlap. But you can also make them by mixing different geometric shapes (e.g., hexagons and squares), to make tessellating patterns. As shown in the figure above, triangles can be used to make a tessellated pattern.
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