![]() 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) 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. There are 8 semi-regular tessellations in total. 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. This wonderfully intuitive resource provides an easy-to-follow guide for students on how to make a tessellation from a square. ![]() To make a regular tessellation, the internal angle of the polygon has to be a diviser of 360. 6, tells us there are 3 vertices with 2 different vertex types. 1 This notation represents (i) the number of vertices, (ii) the number of polygons around each vertex (arranged clockwise) and (iii) the number of sides to each of those polygons. Can Goeun be sure to have found them all?įirstly, there are only three regular tessellations which are triangles, squares, and hexagons. Euclidean tilings are usually named after Cundy & Rollett’s notation. Goeun from Bangok Patana School in Thailand sent in this solution, which includes 8 semi-regular tesselations.
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