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. In the first figure, the tessellation is made up of squares and octagons (8-sided polygons). 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. To make a regular tessellation, the internal angle of the. ![]() Students from Cowbridge Comprehensive School in Wales used this spreadsheet to convince themselves that only 3 polygons can make regular tesselations. Firstly, there are only three regular tessellations which are triangles, squares, and hexagons. 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. Print this grid either by printing the whole webpage, or by right-clicking on it and click on 'Print Picture'. Interesting tessellations may be formed beginning with a square or equilateral triangle. ![]() Trihedral tilingtessellation using three different congruent figures. Grids - triangle - square - hexagon - sq & tri - hex & tri - hex, sq & tri - oct & sq - dodeca & tri - dodeca, hex & sq - pentagons - waffle - fish. A tessellation may be created using slides, flips, and turns. ![]() Dihedral tilingtessellation using two different congruent figures. Monohedral tilingtessellation made up of congruent copies of one figure. To make a regular tessellation, the internal angle of the polygon has to be a diviser of 360. Use the angle measures from part (b) to explain why the tessellation is possible. Tessellationcovering, or tiling, of a plane with a pattern of figures so there are no or gaps. Can Goeun be sure to have found them all?įirstly, there are only three regular tessellations which are triangles, squares, and hexagons. Goeun from Bangok Patana School in Thailand sent in this solution, which includes 8 semi-regular tesselations.
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