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# Tessellations

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Powerpoint display of a tessellation method

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### Tessellations

1. 1. Tessellation is the covering of a flat surface with shapes so there is no space between. This is used in tiling and mosaics, and is a very ancient science. There are many different approaches to tessellating and I will only present one here.
2. 2. If we start off with a random shape and then try to join it up, we find that no matter how hard we try, there are spaces between.
3. 3. So now we make up a new shape, made up of the old one PLUS the space between. And we find that this new shape does tessellate!
4. 4. But we could also have made up a new shape like this. And this tessellates as well!
5. 5. Or this…………
6. 6. Or this……
7. 7. So we have made 4 shapes that tessellate with themselves. And, guess what, they also tessellate with each other!
8. 8. Here’s a few tessellations I designed for using as pavers or tiles. In putting these together I have used an old piece of Mac software called Claris Draw - it’s ideal for this and imports directly into PowerPoint.
9. 9. Two pavers - self tessellating or tessellating with each other Slide 1
10. 10. Four pavers - Each can tessellate with itself or combine to produce a 4 shape tessellation Slide 2
11. 11. Five sided paver - Tessellation achieved by progressive 180 degree rotations Slide 3
12. 12. Two pavers - each Self- tessellating or combined to produce 3d tessellating effect Slide 4
13. 13. Highly interlocked tessellation Five sided paver with tessellation achieved by progressive 180 degree rotations to produce an undulating effect Slide 5
14. 14. Tessellation achieved by progressive 90 degree rotations Slide 6
15. 15. Highly interlinked tessellation Slide 7
16. 16. Two pavers each self tessellating by progressive 180 degree row rotations or tessellating in pairs using the same technique Slide 8
17. 17. Tessellation achieved by progressive 180 degree rotations Slide 9
18. 18. Tessellation achieved by progressive 180 degree rotations Slide 10
19. 19. Circular pattern can be tessellated in several ways