![]() All semi-regular tessellations require either the triangle or a quadrangle such as a square, and there are eight possible combinations. SEMI-REGULAR, which feature the use of two or more shapes.No other shapes can form a regular tessellation. Only three polygons fall into this category: triangles, quadrangles and hexagons. REGULAR, which feature the use of only one shape or polygon.Who wants a hole in their beautifully tiled floor?įurther, there are two basic types of tessellations: This makes perfect sense if either of these two rules are broken, your tessellation will have a gap somewhere. The interior angles of all convergent corner points must add up to 360 degrees to complete a circle.ALL shapes or polygons forming the tessellation must meet at a vertex.The corner points at which tessellated tiles meet is called a vertex. The pattern must be continuous throughout. ![]() The golden rule is that NO gaps are allowed. The number of shapes involved does not matter: you can use only one shape, as per the square above or you can use many more than one polygon. The simplest definition of tessellation is to cover a surface by repeated use of geometric shapes or polygons. The square, diamond and ogee shapes are everywhere – hello again, drop repeats! – because four is such an important number. One of the most common, versatile, and easiest tessellations involves tiled squares, each meeting at the corner to form a group of four. The verb “tessellate” is derived from the Greek tessares, meaning four – which leads us back to tile formation. ![]() Diamond and ogee tessellations can also accommodate drop repeats. Drop repeats are formed by quadrangles, and in this case the drop repeat features square shapes. The Parquet cowl features half-drop repeats AND a square tessellation. Last week you may have noticed that drop repeats can only be created with four-sided shapes, or polygons whose sides are a multiple of four, and this gives us another clue about the origins of tessellation. To get the most out of tessellations, it’s best to move away from texture and into the world of colour think intarsia and stranded colourwork. If the leaf motifs are the trees, planted at half-drop intervals, then tessellation is the wood, showing us the overall shape and character. Tessellations refer to the geometric plan of the pattern as a whole. Translations such as drop repeats and reflections relate to the details, textures or images that make up a pattern. It is one thing to talk about how a leaf motif can be duplicated across a surface, but the other half of the story is the geometry of that repetition. Last month I discussed drop repeats, which are related to tessellations, but they are only half the story. ![]() Although tessellation can be found in any branch of surface pattern design, quilting is one of the most prominent examples of tessellation in the world of arts and crafts – tiling notwithstanding. See this article for more on the notation introduced in the problem, of listing the polygons which meet at each point.If you’re a quilter, you’ll have a head start on today’s post tessellations are a crucial part of pattern repeat design. 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. To make a regular tessellation, the internal angle of the polygon has to be a diviser of 360. 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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