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.


I pentomino and X2 hexomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (26x60):

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
1-25
26
N>0
1-25
?
26
?
?
27
?
?
?
28
?
?
?
29
?
?
?
30
?
?
?
31
?
?
?
32
?
?
?
33
?
?
?
34
?
?
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35
?
?
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36
?
?
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37
?
?
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38
?
?
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39
?
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40
?
?
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41
?
?
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42
?
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43
?
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44
?
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45
?
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?
46
?
?
?
47
?
?
?
48
?
?
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49
?
?
?
50
?
?
?
51
?
?
?
52
?
?
?
53
?
?
?
54
?
?
?
55
?
?
?
56
?
?
?
57
?
?
?
58
?
?
?
59
?
?
?
60
?
≥1
?
N>0
?
?

See Also

I pentomino and W2 hexominoI pentomino and Y1 hexomino