Tiling with 20-fold symmetry (n=10)
The tiling for n=10 showing 20-fold symmetry is shown below.
The following pictures show at least the first 3 iterations of each of the 35 tiles.
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Tiile 1 and inflations 1-5 PDF |
Tile 1 inflation 6 PDF |
Tile 1 inflation 7 PDF |
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Tile 2 and inflations 1-5 PDF |
Tile 2 inflation 6 PDF |
Tile 3 and inflations 1-5 PDF |
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Tile 4 and inflations 1-4 PDF |
Tile 5 and inflations 1-3 PDF |
Tile 6 and inflations 1-3 PDF |
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Tile 7 and inflations 1-2 PDF |
Tile 7 inflation 3 PDF |
Tile 8 and inflations 1-3 PDF |
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Tile 9 and inflations 1-2 PDF |
Tile 9 inflation 3 PDF |
Tile 10 and inflations 1-2 PDF |
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Tile 10 inflation 3 PDF |
Tile 11 and inflation 1 PDF |
Tile 11 inflation 2 PDF |
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Tile 11 inflation 3 PDF |
Tile 12 and inflations 1-3 PDF |
Tile 13 and inflations 1-2 PDF |
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Tile 13 inflation 3 PDF |
Tile 14 and inflations 1-3 PDF |
Tile 15 and inflations 1-2 PDF |
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Tile 15 inflation 3 PDF |
Tile 16 and inflations 1-2 PDF |
Tile 16 inflation 3 PDF |
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Tile 17 and inflation 1 PDF |
Tile 17 inflation 2 PDF |
Tile 17 inflation 3 PDF |
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Tile 18 and inflations 1-2 PDF |
Tile 18 inflation 3 PDF |
Tile 19 and inflation 1 PDF |
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Tile 19 inflation 2 PDF |
Tile 19 inflation 3 PDF |
Tile 20 and inflations 1-2 PDF |
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Tile 20 inflation 3 PDF |
Tile 21 and inflation 1 PDF |
Tile 21 inflation 2 PDF |
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Tile 21 inflation 3 PDF |
Tile 22 and inflations 1-2 PDF |
Tile 22 inflation 3 PDF |
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Tile 23 and inflation 1 PDF |
Tile 23 inflation 2 PDF |
Tile 23 inflation 3 PDF |
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Tile 24 and inflations 1-2 PDF |
Tile 24 inflation 3 PDF |
Tile 25 and inflations 1 PDF |
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Tile 25 inflation 2 PDF |
Tile 25 inflation 3 PDF |
Tile 26 and inflations 1-2 PDF |
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Tile 26 inflation 3 PDF |
Tile 27 and inflation 1 PDF |
Tile 27 inflation 2 PDF |
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Tile 27 inflation 3 PDF |
Tile 28 and inflation 1-2 PDF |
Tile 28 inflation 3 PDF |
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Tile 29 and inflation 1 PDF |
Tile 29 inflation 2 PDF |
Tile 29 inflation 3 PDF |
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Tile 30 and inflations 1-3 PDF |
Tile 31 and inflations 1-2 PDF |
Tile 31 inflation 3 PDF |
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Tile 32 and inflations 1-2 PDF |
Tile 32 inflation 3 PDF |
Tile 33 and inflation1 PDF |
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Tile 33 inflation 2 PDF |
Tile 33 inflation 3 PDF |
Tile 34 and inflations 1-2 PDF |
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Tile 34 inflation 3 PDF |
Tile 35 and inflation 1 PDF |
Tile 35 inflation 2 PDF |
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Tile 35 inflation 3 PDF |
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Periodic tiles and fixed points
There are 3 sets of period-6 tiles shown in the last 3 rows (except for the light green at the end of row 2, tiles 16 and 17). These sets are the tiles numbered as tiles 18-23, 24-29, and 30-35. Each tile’s inflation has at its center the next tile in the sequence, until the sixth tile that has the first tile at its center.
There is one fixed point vertex pattern in the tiling, emerging at every vertex, where the mandala below emerges with higher iterations. This mandala was created using the fifth iteration of the thin rhomb.
Back to Filling the Gaps n-fold tiling
Copyright 2020 by Jim Millar