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 G hexomino

Prime rectangles: 83.

Smallest rectangle tilings

Smallest rectangle (10x12):

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
1-7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
N>0
1-7
0
8
0
0
9
0
0
0
10
0
0
0
0
11
0
0
0
0
0
12
0
0
0
2
4
12
13
0
0
0
0
0
28
0
14
0
0
0
0
4
≥1
≥1
≥1
15
0
0
0
0
0
≥1
0
≥1
0
16
0
0
2
224
514
≥1
≥1
≥1
≥1
≥1
17
0
0
0
8
0
≥1
0
≥1
0
≥1
0
18
0
0
0
8
340
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
0
0
0
≥1
0
≥1
0
≥1
0
≥1
0
20
0
0
114
14042
38794
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
0
668
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
22
0
0
4
948
22144
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
23
0
0
0
48
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
24
0
0
4452
693926
2382274
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
25
0
0
0
35644
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
26
0
0
320
63360
1300608
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
27
0
2
0
3488
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
28
0
4
152188
30496540
132075594
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
29
0
6
0
1606204
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
30
0
8
14948
3276814
71058788
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
31
0
60
0
174832
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
32
0
144
4844886
1.25354261×10¹⁰
6.89236646×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
33
0
268
0
66754012
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
34
0
442
553808
148133648
3.68467109×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
35
0
1434
0
7654456
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
36
0
3552
146965702
4.93751114×10¹¹
3.45601742×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
37
0
7458
0
2.64679351×10¹⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
38
0
14086
18249244
6.19694788×10¹⁰
1.84097698×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
39
0
33832
0
313314420
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
40
0
79582
4.30628288×10¹⁰
1.88844902×10¹³
1.68486627×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
41
0
174196
0
1.01708600×10¹²
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
42
0
354768
562935688
2.46941204×10¹²
8.95426086×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
43
0
776282
0
1.23071014×10¹¹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
44
0
1732740
1.23031804×10¹²
7.06945649×10¹⁴
8.04509945×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
45
0
3791452
0
3.82114400×10¹³
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
46
0
7982782
1.66629730×10¹¹
9.52266078×10¹³
4.26877634×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
47
0
17051550
0
4.69925694×10¹²
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
48
0
36926110
3.44930143×10¹³
2.60362917×10¹⁶
3.78080070×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
49
0
79825434
0
1.41129394×10¹⁵
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
50
0
169702980
4.79513804×10¹²
3.58677412×10¹⁵
2.00386282×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
51
0
360439984
0
1.75744028×10¹⁴
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
52
0
769452660
9.53059947×10¹⁴
9.46676488×10¹⁷
1.75460440×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
53
0
1.64523091×10¹⁰
0
5.14330601×10¹⁶
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
54
0
3.49627288×10¹⁰
1.35180375×10¹⁴
1.32731181×10¹⁷
9.29214789×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
55
0
7.40771036×10¹⁰
0
6.46891916×10¹⁵
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
56
0
1.57068970×10¹¹
2.60306597×10¹⁶
3.40667838×10¹⁹
8.06048703×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
57
0
3.33367434×10¹¹
0
1.85441829×10¹⁸
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
58
0
7.06091328×10¹¹
3.75145558×10¹⁵
4.84468061×10¹⁸
4.26629328×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
59
0
1.49235341×10¹²
0
2.35146000×10¹⁷
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
60
0
3.15215537×10¹²
7.04303534×10¹⁷
1.21551532×10²¹
3.67199001×10²²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
61
0
6.65863850×10¹²
0
6.62747344×10¹⁹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
62
0
1.40545261×10¹³
1.02824669×10¹⁷
1.74892977×10²⁰
1.94274661×10²²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
63
0
2.96282750×10¹³
0
8.46132819×10¹⁸
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
64
0
6.24081092×10¹³
1.89076774×10¹⁹
4.30615253×10²²
1.66106127×10²⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
65
0
1.31408642×10¹⁴
0
2.35121441×10²¹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
66
0
2.76561945×10¹⁴
2.79018535×10¹⁸
6.25694273×10²¹
8.78576564×10²³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
67
0
5.81614333×10¹⁴
0
3.01928118×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
68
0
1.22230910×10¹⁵
5.04255480×10²⁰
1.51629241×10²⁴
7.46910991×10²⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
69
0
2.56757153×10¹⁵
0
8.28945761×10²²
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
70
0
5.39110334×10¹⁵
7.50872698×10¹⁹
2.22170159×10²³
3.94987143×10²⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
71
0
1.13137550×10¹⁶
0
1.06983503×10²²
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
72
0
2.37304384×10¹⁶
1.33724883×10²²
5.31139637×10²⁵
3.34126994×10²⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
73
0
4.97518014×10¹⁶
0
2.90691571×10²⁴
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
74
0
1.04265255×10¹⁷
2.00666184×10²¹
7.83870290×10²⁴
1.76675836×10²⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
75
0
2.18419612×10¹⁷
0
3.76818582×10²³
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
76
0
4.57363070×10¹⁷
3.52901823×10²³
1.85209109×10²⁷
1.48800429×10²⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
77
0
9.57325577×10¹⁷
0
1.01465465×10²⁶
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
78
0
2.00310034×10¹⁸
5.33096027×10²²
2.75062649×10²⁶
7.86765997×10²⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
79
0
4.18980739×10¹⁸
0
1.32041307×10²⁵
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
80
0
8.76060953×10¹⁸
9.27350181×10²⁴
6.43258056×10²⁸
6.60060999×10³⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
81
0
1.83116874×10¹⁹
0
3.52722843×10²⁷
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
82
0
3.82635188×10¹⁹
1.40901579×10²⁴
9.60645916×10²⁷
3.48995921×10³⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
83
0
7.99299082×10¹⁹
0
4.60616196×10²⁶
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
84
0
1.66918503×10²⁰
2.42773940×10²⁶
2.22626570×10³⁰
2.91774763×10³²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
85
0
3.48476673×10²⁰
0
1.22175678×10²⁹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
86
0
7.27314463×10²⁰
3.70759495×10²⁵
3.34114797×10²⁹
1.54274440×10³²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
87
0
1.51759040×10²¹
0
1.60050657×10²⁸
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
88
0
3.16573200×10²¹
6.33449471×10²⁷
7.68076684×10³¹
1.28575924×10³⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
89
0
6.60212738×10²¹
0
4.21836348×10³⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
90
0
1.37653554×10²²
9.71783079×10²⁶
1.15781700×10³¹
6.79873184×10³³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
91
0
2.86938148×10²²
0
5.54192696×10²⁹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
92
0
5.97984046×10²²
1.64788706×10²⁹
2.64246377×10³³
5.65013696×10³⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
93
0
1.24593117×10²³
0
1.45230077×10³²
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
94
0
2.59540100×10²³
2.53829078×10²⁸
3.99919012×10³²
2.98785059×10³⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
95
0
5.40534795×10²³
0
1.91299348×10³¹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
96
0
1.12552272×10²⁴
4.27542318×10³⁰
9.06798148×10³⁴
2.47664847×10³⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
97
0
2.34314252×10²⁴
0
4.98707749×10³³
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
98
0
4.87707366×10²⁴
6.60953973×10²⁹
1.37733760×10³⁴
1.30979608×10³⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
99
0
1.01493539×10²⁵
0
6.58498013×10³²
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
100
0
2.11172897×10²⁵
1.10656969×10³²
3.10465016×10³⁶
1.08312332×10³⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
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See Also

I tetromino and C hexominoI tetromino and T1 hexomino