# Taking a Look at Tessellations

1367 WordsFeb 4, 20185 Pages
Most people recognize the artistry of walls in ancient palaces, of mosaic pictures, and even of honeycombs. Likewise, the artistry and intricacies of M.C. Escher's drawings astound most people. When we look at these objects and artwork we recognize the shapes within them; we see squares, hexagons and other shapes without giving them much thought. We might not even know that these patterns of shapes have a name, and we certainly do not think of mathematics when we see them. But, in fact, these patterns - or tessellations - are part of the field of geometry. When a space is covered with a pattern of flat shapes with no overlaps or gaps it is known as a tessellation or a tilling. Tessellations have been around for many centuries and in many different cultures and are still prevalent today. In Latin the word tesserae means small stone cube they were used to make up tessellata- the mosaic pictures forming floors and tiling in Roman buildings. Making a repeating pattern with a regular polygon creates regular tessellations. Triangles, squares and hexagons are the only three shapes that can make a regular tessellation. In order for a tessellation to be regular the pattern is identical at each vertex. A tessellation created with two or more regular polygons is known as a semi-regular tessellation. Just like in a regular tessellation in a semi-regular tessellation the pattern at each vertex is the same. The third type of tessellation is a demi regular tessellation however