Conclusion – squares can tessellate a surface uniformly while pentagons cannot. The interior angle is 108° and number of sides meeting at the vertex is 3. On the other hand, for an irregularly tessellated figure, it won’t be so.įor example, in case of a square, the interior angle is 90° and the number of sides meeting at each vertex is 4. For a regular tessellation, the product xy will be 360. Then ask them to measure the interior angle of the polygon used for tiling, say y. Also, after the surface is tessellated, ask the kids to count the number of sides that meet at each vertex in the tessellation, say x. Well, regular shapes like triangles, squares, and hexagons tessellate naturally while irregular shapes have to fit into each other to tile a surface uniformly. With this tessellation art, you’ll be bringing together tessellations and math, as the kids will understand the difference between tiling with regular and irregular shapes. But here, you’ll have to ensure that the shapes complement each other, i.e. Or ask the kids to cut irregular shapes for the tessellations. Cut one for them and then ask the kids to cut multiples. You could vary the activity by cutting out shapes of animals and birds. Would you consider it to be the gaps left by the tiled pattern, making this tessellation an semi-regular one? Or would you think of this as a pattern of cross or plus signs fitting into one another, making this a regular tessellation? Observe the white space around each shape. It also led to studies in types of tessellations (regular and semi-regular) and which shapes can be used to make tessellations and how. His work led to further study of tessellations from the mathematical point of view. Federov, a Russian crystallographer proved that tessellation of a plain can be done in any of the 17 groups of isometries. They are closely associated with math and crystallography as well. Tessellations are not limited to just art. Nikolas Schiller is an American map artist known for his kaleidoscopic aerial photography, which can be called an indirect application of tessellations. Examples of tessellations are found in ancient and modern art.Īrtworks of the Dutch graphic artist M.C. Tessellations in the form of tiled walls and flooring are part of ancient architectural styles and designs. The word ‘tessellation’ is derived from the Latin word tessella, which means a small cubical piece of clay, glass, or stone.

Each surface of the cube is a regular tessellation of squares. A Rubik’s cube is an interesting example of tessellations.

Easy tessellation animals