12/28/2023 0 Comments A triangular tessellation definitionNow keep going around the vertex in either direction, finding the number of sides of the polygons until you get back to the polygon you started with. Since it’s a square, it has four sides, and that’s where the first “4” comes from. Here’s how: choose a vertex, and then look at one of the polygons that touches that vertex. For all the others, the interior angles are not exact divisors of 360 degrees, and therefore those figures cannot tile the plane.Ī tessellation of squares is named “ 4.4.4.4“. This works for the triangle, square, and hexagon, and you can show working tessellations for these figures. Since the regular polygons in a tessellation must fill the plane at each vertex, the interior angle must be an exact divisor of 360 degrees. You can work out the interior measure of the angles for each of these polygons: Shape Also, if you look at 6 triangles at a time, they form a hexagon, so the tiling of triangles and the tiling of hexagons are similar and they cannot be formed by directly lining shapes up under each other – a slide (or a glide!) is involved. When you look at these three samples you can easily notice that the squares are lined up with each other while the triangles and hexagons are not. Only three regular polygons tessellate in the Euclidean plane: triangles, squares or hexagons.We can’t show the entire plane, but imagine that these are pieces taken from planes that have been tiled. A regular tessellation means a tessellation made up of congruent regular polygons. The word “tessellate” is derived from the Ionic version of the Greek word “tesseres,” which in English means “four.” The first tilings were made from square tiles.Ī regular polygon has 3 or 4 or 5 or more sides and angles, all equal. A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps.Īnother word for a tessellation is a tiling.Ī dictionary * will tell you that the word “tessellate” means to form or arrange small squares in a checkered or mosaic pattern.
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