POLYOMINO TILINGS

Polyomino Tilings

Select polyominoes for a set (currently 1 or 2), for which tilings should be shown.

Then click "Show" button.

You may also see list of all polyomino sets for which data is available here.


P pentomino and N1 hexomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (2x11):

Rectangle tilings' solutions count (including symmetric)

Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Purple number - prime rectangle (unknown if weakly or strongly prime).

Red number - composite rectangle (which can be divided into two rectangles tileable by this set).

Gray number - it is unknown whether rectangle is prime or composite.

Question mark (?) - solution count is unknown.

Click on underlined numbers to view picture with one solution.

w \ h
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
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20
N>0
1
?
2
?
?
3
?
?
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4
?
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?
5
?
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?
6
?
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7
?
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8
?
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9
?
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10
?
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?
11
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
12
?
?
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?
?
?
?
?
?
?
≥1
?
13
?
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?
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?
?
?
?
14
?
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?
?
?
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≥1
?
?
?
15
?
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?
?
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?
?
?
?
?
?
?
16
?
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≥1
?
?
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17
?
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18
?
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≥1
?
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19
?
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20
?
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?
?
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?
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≥1
?
?
?
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?
21
?
?
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N>0
?
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?
?
?
?
?
?
?
?
?
?
?
?
?

See Also

P pentomino and M hexominoP pentomino and N2 hexomino