![]() Let’s look at a few examples of tessellations below. A classic tessellation is a model which uses a tessellated pattern as its main subject (meaning the tessellation is not used just in an auxiliary role such as creating scales on an animal model). The only rule is that the sides must all sit flush against one another, leaving no gaps or empty spaces at all. A Crease Pattern was published in Techno Origami, book of 15th Origami Outdoor Meeting. Quilting, dressmaking, and history plied with the needle. However, you can also use mixed shapes to create tessellating patterns, such as triangles and hexagons or triangles and squares. "But Karen," I imagine you saying, "Now those circles are bifurcated with new seamlines! It's not the same!" And? So? Therefore? If I didn't want seams through my circles, I'd have to cut wonky-shaped pieces and assemble it in a way that doesn't allow for periodically "squaring up". In step 2, I erase what's outside the square tile and erase two circle-lines so the other circles look like they're on top And in step 3, I color and tile the squares, rotating them as needed to get the pattern I want. If I were making a paper pattern, I'd decide on the length of the radius, measure that distance from the corner along the edge of the square and so find the circle's center, and draw a circle from that center point. As I draw this in MS Paint, I am merely eyeballing it, trusting my eyes to make the edge of the square tile overlap the diameter of the circle and the edge of the circle touch the corner of the square. In the plane, there are eight such tessellations, illustrated above (Ghyka 1977, pp. I pay attention to the size of the circles, and to where they intersect the edges and corners of the square. Regular tessellations of the plane by two or more convex regular polygons such that the same polygons in the same order surround each polygon vertex are called semiregular tessellations, or sometimes Archimedean tessellations. ![]() ![]() ![]() In step 1, I lay down the simplest shapes I see: a square, with four circles. ![]()
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