Pentagonal tile that was unsolved for 30 years
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The 15th monohedral tiling convex pentagon creates an interesting pattern called the double helix. Solve it by yourself!
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- Printables
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- Math
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- Creative Commons — Attribution — Noncommercial
Tessellations were used by the Sumerians (about 4000 BC) in building wall decorations formed by patterns of clay tiles. Nowadays, mathematicians try to solve tesselation rules and try to find more possible arrangements.
One of the challenges is to invent another tile arrangement using pentagons. By the end of the 21st century, 14 of them were known. The 15th monohedral tiling convex pentagon was discovered in 2015 using a computer algorithm. Moreover, it is the last possible.
The geometry of a single tile is quite interesting:
If you use enough amount of tiles, you can get the puzzle arrangement like below:
Finding the proper tile shape takes mathematicians 30 years. Using between 12 and 24 tiles you can try to solve this interesting pattern :)
An interesting article with many pentagonal tiling samples you can find here: https://www.jaapsch.net/tilings/#pentagon
All images are from en.wikipedia.org