It is definitely possible to work with odd-sided polygons, but only on a large scale, and – I’m sticking my neck out here – only with the support of at least one other even-numbered polygon such as a square, diamond or octagon. There’s a good reason why knitters of old stuck to squares and octagons: OXO patterns, Nordic stars. Because knitted fabric is all one piece, shapes like pentagons and heptagons – anything with an odd number of sides or interior angles – are tricky to manage for stitches, which are essentially four-sided shapes. This has a lot to do with the stitch-row ratio and fabric construction. The three regular tessellations, plus any semi-regular tessellation featuring squares, triangles or hexagons, work best. The ability to reduce polygons to triangles is particularly important for knitting because the most successful tessellations always feature polygons with an even number of sides. The triangle is the root of all geometric shapes note that the square root is symbolised by a triangle, diagonal line, or a line cutting across the centre of the square from one corner to the other. With odd-sided polygons, there will always be a corner left over. All can be reduced to triangles if you connect the opposite corners with a line. At the top we have an octagon/square combination, followed by hexagons and diamonds. Only three lines are needed to draw a triangle, and all polygons can be reduced down to a triangle.Įxamples of regular and semi-regular tessellations. It’s worth noting that the triangle is at the root of all tessellations because it is the very first and simplest three-dimensional shape. 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? Two types of tessellationįurther, 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. If you’re a quilter, you’ll have a head start on today’s post tessellations are a crucial part of pattern repeat design.
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