See this article for more on the notation introduced in the problem, of listing the polygons which meet at each point. Hexagons & Triangles (but a different pattern) Triangles & Squares (but a different pattern) Because the tessellation plays a significant role in. Meanwhile, irregular tessellations consist of figures that arent composed of regular polygons that interlock without gaps or overlaps. A chessboard is an example of a simple tessellation the squares meet side to side without gaps. Only eight combinations of regular polygons create semi-regular tessellations. Two- and three-dimensional examples of the tessellations can be seen in contemporary architecture either as façade elements or patterns used for structural elements. Semi-regular tessellations are made from multiple regular polygons. We know each is correct because again, the internal angle of these shapes add up to 360.įor example, for triangles and squares, 60 $\times$ 3 + 90 $\times$ 2 = 360. The tessellation can be reviewed under three categories such as regular, semi-regular and demi-regular tessellations. Triangular tessellation Each polygon is a non-overlapping equilateral triangle. There are 8 semi-regular tessellations in total. There are only three tessellations that are composed entirely of regular, congruent polygons. We can prove that a triangle will fit in the pattern because 360 - (90 + 60 + 90 + 60) = 60 which is the internal angle for an equilateral triangle. Students from Cowbridge Comprehensive School in Wales used this spreadsheet to convince themselves that only 3 polygons can make regular tesselations. For example, we can make a regular tessellation with triangles because 60 x 6 = 360. This is because the angles have to be added up to 360 so it does not leave any gaps. Demi-regular tessellations are those that use non-regular or non-geometric shapes, such as those popularized by M.C. To make a regular tessellation, the internal angle of the polygon has to be a diviser of 360. These have interior angles which are divisors of 360. There are three types of regular tessellations, those being triangles, hexagons, and squares. Can Goeun be sure to have found them all?įirstly, there are only three regular tessellations which are triangles, squares, and hexagons. Regular tessellations: Regular tessellations are tile coverings made up of only one shape. Goeun from Bangok Patana School in Thailand sent in this solution, which includes 8 semi-regular tesselations.
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