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.


Dominoes and W pentomino

Prime rectangles: 12.

Smallest rectangle tilings

Smallest rectangle (3x6):

Smallest square (5x5):

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
19
20
1-2
0
3
0
0
4
0
0
0
5
0
0
4
40
6
0
2
14
244
1846
7
0
0
78
1192
15706
138608
8
0
20
284
7098
109433
≥1
≥1
9
0
0
1112
26900
770300
≥1
≥1
≥1
10
0
130
3918
159826
5098706
≥1
≥1
≥1
≥1
11
0
0
13764
548292
33415334
≥1
≥1
≥1
≥1
≥1
12
0
714
46624
3202518
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
0
3598
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
17222
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
79684
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
359966
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
2k
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all
all
all
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See Also

Dominoes and V pentominoDominoes and X pentomino