Fractal Tilings for which the Prototile may be Generated by Dissecting a Polyhex
The search for polyhexes that yield prototiles admitting f-tiling is greatly simplified by realizing some requirements they must satisfy. For a brief discussion of this topic, click here.
The following table shows the lower-order polyhexes (blue) that possess 2- or 3-fold rotational symmetry (the only types that work), along with candidate prototiles derived by dissecting them. The red prototiles admit one or more f-tilings, while the black prototiles do not admit f-tilings. Click on the red prototiles below to see the f-tiling(s) based on the prototile.
After the table, there are links to f-tilings based on higher-order polyhexes.
1-hex:
2-hex:
1st 3-hex:
2nd 3-hex:
1st 4-hex:
2nd 4-hex:
3rd 4-hex:
4th 4-hex:
Some f-tilings generated from higher-order polyhexes follow.
A 6-hex f-tiling:
A 7-hex f-tiling:
A 7-hex f-tiling using a prototile generated by a different dissection of the same 7-hex:
A 9-hex f-tiling:
A 10-hex f-tiling:
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