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 triomino and Z tetromino

Prime rectangles: 29.

Smallest rectangle tilings

Smallest rectangles and smallest square (4x9, 6x6):

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
1-3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1-3
0
4
0
0
5
0
0
0
6
0
0
0
4
7
0
0
0
34
0
8
0
0
40
84
320
8204
9
0
16
54
370
4750
27602
≥1
10
0
0
12
1446
3346
84832
≥1
≥1
11
0
8
756
4374
43114
1184554
≥1
≥1
≥1
12
0
188
1062
15458
361460
≥1
≥1
≥1
≥1
≥1
13
0
2
472
≥5000
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
14
0
112
≥5000
≥5000
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
1600
≥5000
≥5000
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
74
≥5000
≥5000
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
1242
≥5000
≥5000
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
≥5000
≥5000
≥5000
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
1364
≥5000
≥5000
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
≥5000
≥5000
≥5000
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
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all
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all
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See Also

I triomino and T tetrominoI triomino and I pentomino