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Here are some of the lovely designs you've made. Click on each design to enlarge the picture. Back to main tiles page.
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 tiling 3.4.6.4 |
 tiling 3.4.6.4/4.6.12 |
 central pattern, 3 symmetry axes |
 tiling 3.12.12/3.4.3.12 |
 tiling 4.6.12 |
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 central pattern, 6 symmetry axes |
 central pattern, rotation symmetry order 6 |
 frieze |
 tiling 3.3.3.3.3.3/3.3.4.12 |
 tiling 3.6.3.6 |
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 (the centre apart), central pattern, 12 symmetry axes |
 central pattern, 6 symmetry axes |
 tilings 3.3.4.3.4/3.3.4.12/4.6.12 & 3.4.6.4/4.6.12 |
 central pattern, 6 symmetry axes |
 central patterns, 6 symmetry axes |
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 central patterns: 2 symmetry axes, 6 symmetry axes, rotation symmetry order 3 |
 tiling 3.3.4.3.4/3.4.3.12/3.3.4.12 |
 tiling 3.12.12 |
 central pattern, 6 symmetry axes |
 tiling 4.8.8 within 3.12.12/3.4.3.12 |
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 central pattern, rotation symmetry order 6 |
 central pattern, 12 symmetry axes |
 central pattern, 6 symmetry axes |
 central pattern, 4 symmetry axes |
 tiling 3.4.4.6/3.6.3.6 |
All these designs are made with regular polygons except for a few, which include 30-degree and 60-degree rhombuses and the trapezia you get by cutting regular hexagons in half.
Under the pictures we’ve used ‘tiling’ to mean ‘tessellation’.
Can you guess what, for example, ‘3.3.4.3.4’ or ‘3.4.6.4’ mean?
And what would ‘3.3.4.3.4/3.4.6.4’ mean?
Tessellations really go on for ever in all directions but sometimes you’ve made your tilings look nice by adding borders. We don’t mention those in our titles.
In one case the tiling doesn’t repeat downwards but only to left and right. Such a pattern is called a frieze.
Your patterns with a centre have symmetry elements, for example axes of reflection symmetry (‘mirror lines’). Because your patterns have at least 2 mirror lines they also possess rotation symmetry. But particularly interesting are the patterns which don’t have mirror symmetry but do have rotation symmetry.
It’s important to realise that such central patterns can be found all over your tessellations: imagine that you’d duplicated hundreds of the patterns in the hexagonal trays and packed them together.

The Magic Mathworks Travelling Circus
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T: 01352 713014 or 07774 997177
E: pstephenson1@mac.com
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