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 W pentomino

Prime rectangles: 83.

Smallest rectangle tilings

Smallest rectangle (8x11):

Smallest square (12x12):

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
1-5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
N>0
1-5
0
6
0
0
7
0
0
0
8
0
0
0
0
9
0
0
0
0
0
10
0
0
0
0
0
0
11
0
0
0
2
0
32
0
12
0
0
0
4
46
118
608
≥1000
13
0
0
0
6
0
2
0
≥1000
176
14
0
0
0
8
0
0
≥1000
≥1000
≥1000
≥1
15
0
0
0
120
0
3632
116
≥1000
≥1000
≥1
≥1
16
0
2
4
270
3536
15936
≥1000
≥1000
≥1000
≥1
≥1
≥1
17
0
0
4
462
168
734
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
18
0
0
0
705
106
218
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
19
0
0
4
3446
20
253326
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
20
0
34
76
8433
164686
1198669
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
116
16596
20768
102704
≥4000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
22
0
0
2
29416
12596
41458
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
23
0
0
132
85646
2516
14335574
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
24
0
366
948
208046
6334164
69890200
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
25
0
0
1948
442484
1414368
9592394
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
26
0
0
166
869974
846740
4476782
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
27
0
0
2416
2056926
175232
726999960
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
28
0
3258
10206
4757584
220643320
3.56611651×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
29
0
0
25644
10361262
71230484
718897868
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
30
0
0
6162
21536136
42610368
367025670
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
31
0
0
33124
47400674
9069084
3.45882188×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
32
0
26344
104024
105170137
7.21462449×10¹⁰
1.68490730×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
33
0
2
300520
228435042
2.98930390×10¹⁰
4.68139895×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
34
0
0
146064
485268987
1.79811980×10¹⁰
2.55801622×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
35
0
0
384800
1.04434307×10¹⁰
395375764
1.58070747×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
36
0
201642
1033022
2.26223592×10¹⁰
2.25550502×10¹²
7.58811024×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
37
0
90
3328404
4.86940590×10¹⁰
1.11402715×10¹²
2.75930485×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
38
0
0
2601926
1.03883446×10¹¹
6.76381028×10¹¹
1.60269564×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
39
0
0
4041624
2.21797808×10¹¹
1.55415803×10¹¹
7.02981103×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
40
0
1490254
10035358
4.74592882×10¹¹
6.81993314×10¹³
3.30943047×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
41
0
2150
35618644
1.01352369×10¹²
3.83006261×10¹³
1.50889589×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
42
0
0
38161166
2.15724702×10¹²
2.35350480×10¹³
9.31049976×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
43
0
0
39843156
4.58545698×10¹²
5.72574677×10¹²
3.06534697×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
44
0
10744926
95217738
9.74678916×10¹²
2.01025905×10¹⁵
1.41079512×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
45
0
36486
369900304
2.06980839×10¹³
1.24458963×10¹⁵
7.78511887×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
46
0
0
487590892
4.38910101×10¹³
7.75658620×10¹⁴
5.10989208×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
47
0
0
376971684
9.29621902×10¹³
2.02012362×10¹⁴
1.31669002×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
48
0
76036326
882072070
1.96765580×10¹⁴
5.80907208×10¹⁶
5.91300108×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
49
0
496060
3.72753827×10¹⁰
4.16176258×10¹⁴
3.88380264×10¹⁶
3.83671998×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
50
0
4
5.63279723×10¹⁰
8.79488766×10¹⁴
2.45920223×10¹⁶
2.68252748×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
51
0
2
3.46997247×10¹⁰
1.85703680×10¹⁵
6.90492778×10¹⁵
5.58854794×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
52
0
530184736
7.99223859×10¹⁰
3.91836290×10¹⁵
1.65245535×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
53
0
5771628
3.64838940×10¹¹
8.26260891×10¹⁵
1.17630076×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
54
0
220
6.03520147×10¹¹
1.74116694×10¹⁶
7.57814772×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
55
0
114
3.13465502×10¹¹
3.66685382×10¹⁶
2.30077933×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
56
0
3.65294725×10¹⁰
7.10635180×10¹¹
7.71768708×10¹⁶
4.64136678×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
57
0
59887256
3.47762823×10¹²
1.62348368×10¹⁷
3.48307664×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
58
0
6344
6.10681948×10¹²
3.41324887×10¹⁷
2.28557057×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
59
0
3390
2.79611746×10¹²
7.17247635×10¹⁷
7.50063408×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
60
0
2.49215131×10¹¹
6.22650314×10¹²
1.50645854×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
61
0
569782182
3.23993828×10¹³
3.16262350×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
62
0
128128
5.91355560×10¹³
6.63644178×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
63
0
70286
2.47463511×10¹³
1.39199396×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
64
0
1.68616940×10¹²
5.40067781×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
65
0
5.06905388×10¹⁰
2.96141093×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
66
0
2042196
5.53526593×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
67
0
1145320
2.18198738×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
68
0
1.13277466×10¹³
4.65908350×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
69
0
4.27730224×10¹¹
2.66490340×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
70
0
27433824
5.04743559×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
71
0
15671098
1.92382583×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
72
0
7.56320457×10¹³
4.01586134×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
73
0
3.45965370×10¹²
2.36811349×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
74
0
323839488
4.51199490×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
75
0
187775960
1.70138319×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
76
0
5.02239176×10¹⁴
3.47267678×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
77
0
2.70391037×10¹³
2.08345238×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
78
0
3.45710067×10¹⁰
3.97454712×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
79
0
2.02831038×10¹⁰
1.51287662×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
80
0
3.31910613×10¹⁵
3.02275874×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
81
0
2.05457311×10¹⁴
1.81879029×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
82
0
3.40802974×10¹¹
3.46532009×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
83
0
2.01707366×10¹¹
1.35472753×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
84
0
2.18402392×10¹⁶
2.65456772×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
85
0
1.52511819×10¹⁵
1.57846589×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
86
0
3.15161303×10¹²
3.00184937×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
87
0
1.87616479×10¹²
1.22257975×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
88
0
1.43154871×10¹⁷
2.35470296×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
89
0
1.11015129×10¹⁶
1.36424876×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
90
0
2.76738397×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
91
0
1.65222636×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
92
0
9.35035648×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
93
0
7.94823827×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
94
0
2.32941757×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
95
0
1.39077956×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
96
0
6.08784207×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
97
0
5.61086946×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
98
0
1.89386316×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
99
0
1.12751623×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all

See Also

I tetromino and V pentominoI tetromino and X pentomino