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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