A tessellation is an arrangement of tiles fitting exactly together which can be extended as far as required in any direction.
Here are two tessellations:
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First make a square. Paint has a tool for making rectangles but it doesn't have one for drawing exact squares. Here is one way.
Open paint and select Image and then Attributes. | ![]() |
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In the Attributes box set the image size to 150 by 150 pixels. | ![]() |
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Now colour this square in but keep it reasonably symmetrical. Make sure you save it as somewhere safe with a sensible name. | ![]() |
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Now select and copy the whole of your square and paste several copies of it onto a new Paint document. You can tesselate the plane by using exact copies of your square or by building rectangles from it using symmetry transformations such as reflection or rotation. |
Translation![]() |
Translation and Reflection.![]() |
Translation and Rotation.![]() |
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Any quadrilateral will tile the plane. You have done this with squares. Try the following shapes. These are arranged in order of difficulty. This picture shows the start of a tiling that uses darts. If you examine it then you can see how to tile using rhombi and parallelograms. | ![]() |
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Any quadrilateral will tile the plane. | ![]() |
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Join the quads together. | ![]() |
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Make lots of copies and join them together. | ![]() |
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Now colour the vertices with different colours and the body in yet another colour. Now develop a tile which produces an interesting pattern when you tesselate it. You might want to start with a photograph and cut sections out of it. | ![]() |