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 tetromino and A hexomino

Prime rectangles: ≥ 6.

Smallest rectangle tilings

Smallest rectangle and smallest square (4x4):

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
N>0
1-2
0
3
0
0
4
0
0
8
5
0
0
16
0
6
0
0
24
0
0
7
0
0
66
0
0
0
8
0
6
164
524
1344
8190
61474
9
0
0
340
0
0
0
259102
0
10
0
0
696
0
0
0
951048
0
0
11
0
0
1488
0
0
0
4800408
0
0
0
12
0
32
3268
15954
60790
1032580
27465250
212294070
1.35755876×10¹⁰
1.73582213×10¹¹
2.90308511×10¹²
13
0
0
6994
0
0
0
126927316
0
0
0
2.74304022×10¹³
?
14
0
0
14580
0
0
0
541767960
0
0
0
2.25732953×10¹⁴
?
?
15
0
0
30830
0
0
0
2.61115267×10¹⁰
0
0
0
2.59183664×10¹⁵
?
?
?
16
0
136
66092
480138
2691682
132269562
1.33995246×10¹¹
1.79255973×10¹²
1.95814675×10¹³
6.54685039×10¹⁴
3.47229633×10¹⁶
≥1
≥1
≥1
≥1
17
0
0
140448
0
0
0
6.35880257×10¹¹
0
0
0
3.57235201×10¹⁷
?
?
?
≥1
?
18
0
0
296296
0
0
0
2.89603519×10¹²
0
0
0
3.35161781×10¹⁸
?
?
?
≥1
?
?
19
0
0
627374
0
0
0
1.37992167×10¹³
0
0
0
3.68941857×10¹⁹
?
?
?
≥1
?
?
?
20
0
538
1333180
14422230
118889530
1.70142181×10¹¹
6.77460293×10¹³
1.52557340×10¹⁵
2.83052980×10¹⁶
2.50655888×10¹⁸
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
2828634
0
0
0
3.23395112×10¹⁴
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
22
0
0
5989024
0
0
0
1.51344501×10¹⁵
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
23
0
0
12687178
0
0
0
7.19875592×10¹⁵
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
24
0
2066
26907640
433074694
5.24968619×10¹⁰
2.19097490×10¹³
3.47152359×10¹⁶
1.30088851×10¹⁸
4.09344517×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
25
0
0
57055156
0
0
0
1.65783642×10¹⁷
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
26
0
0
120901452
0
0
0
7.84514569×10¹⁷
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
27
0
0
256208896
0
0
0
3.73332902×10¹⁸
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
28
0
7824
543131372
1.30038097×10¹¹
2.31796406×10¹²
2.82211382×10¹⁵
1.78756104×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
29
0
0
1.15135853×10¹⁰
0
0
0
8.53116763×10¹⁹
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
30
0
0
2.44027074×10¹⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
31
0
0
5.17203226×10¹⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
32
0
29424
1.09628763×10¹¹
3.90458236×10¹²
1.02347662×10¹⁴
3.63527736×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
33
0
0
2.32376967×10¹¹
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
34
0
0
4.92539221×10¹¹
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
35
0
0
1.04396028×10¹²
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
36
0
110258
2.21277717×10¹²
1.17240567×10¹⁴
4.51906794×10¹⁵
4.68280991×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
37
0
0
4.69023463×10¹²
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
38
0
0
9.94136738×10¹²
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
39
0
0
2.10715059×10¹³
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
40
0
412378
4.46629749×10¹³
3.52031174×10¹⁵
1.99535318×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
41
0
0
9.46675245×10¹³
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
42
0
0
2.00656445×10¹⁴
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
43
0
0
4.25308851×10¹⁴
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
44
0
1540792
9.01480497×10¹⁴
1.05702270×10¹⁷
8.81029965×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
45
0
0
1.91077130×10¹⁵
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
46
0
0
4.05005386×10¹⁵
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
47
0
0
8.58445295×10¹⁵
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
48
0
5753864
1.81955244×10¹⁶
3.17385807×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
49
0
0
3.85670730×10¹⁶
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
50
0
0
8.17464171×10¹⁶
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
51
0
0
1.73268929×10¹⁷
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
52
0
21480810
3.67259194×10¹⁷
9.52995146×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
53
0
0
7.78439221×10¹⁷
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
54
0
0
1.64997260×10¹⁸
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
55
0
0
3.49726653×10¹⁸
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
56
0
80181666
7.41277354×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
57
0
0
1.57120462×10¹⁹
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
58
0
0
3.33031076×10¹⁹
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
59
0
0
7.05889576×10¹⁹
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
60
0
299270432
1.49619698×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
61
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
62
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
63
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
64
0
1.11694921×10¹⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
65
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
66
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
67
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
68
0
4.16862473×10¹⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
69
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
70
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
71
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
72
0
1.55577463×10¹¹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
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≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
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≥1
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≥1
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≥1
≥1
≥1
?
73
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
74
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
75
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
76
0
5.80627538×10¹¹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
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≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
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≥1
≥1
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≥1
≥1
≥1
?
77
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
78
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
79
0
0
≥1.84467440×10²⁰
0
0
0
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0
0
0
≥1.84467440×10²⁰
?
?
?
≥1
?
?
?
≥1
?
80
0
2.16694055×10¹²
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
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≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
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?
N>0
x
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

See Also

I tetromino and Z pentominoI tetromino and C hexomino