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 C heptomino

Prime rectangles: ≥ 57.

Smallest rectangle tilings

Smallest rectangle (10x11):

Smallest known square (20x20):

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
N>0
1-7
0
8
0
0
9
0
0
0
10
0
0
0
0
11
0
0
0
1
0
12
0
0
0
0
0
0
13
0
0
0
0
0
1
?
14
0
0
0
0
119
2
?
?
15
0
0
0
36
0
7
?
?
?
16
0
0
0
4
9
26
?
?
?
?
17
0
0
0
0
0
237
?
?
?
?
?
18
0
0
0
1
8733
588
?
?
?
?
?
?
19
0
2
0
1367
0
6835
?
?
?
≥1
?
≥1
?
20
0
4
12
324
1086
17918
?
?
≥1
≥1
≥1
≥1
≥1
≥1
21
0
6
0
2
0
51483
?
?
?
≥1
?
≥1
?
≥1
?
22
0
8
0
42
526500
124372
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
23
0
50
0
53078
0
972470
?
≥1
?
≥1
?
≥1
?
≥1
?
24
0
124
588
16484
77734
3031518
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
25
0
238
0
137
0
8506457
?
?
?
≥1
?
≥1
?
≥1
?
26
0
400
0
1619
28764416
21485478
?
?
?
≥1
?
≥1
≥1
≥1
?
27
0
1150
0
2015710
0
108696079
?
?
?
≥1
?
≥1
?
≥1
?
28
0
2864
21332
721536
4617271
370936019
?
?
?
≥1
≥1
≥1
≥1
≥1
?
29
0
6166
0
6478
542
1.11316427×10¹⁰
?
?
?
≥1
?
≥1
≥1
≥1
?
30
0
11888
0
63211
1.48402690×10¹⁰
3.02702436×10¹⁰
?
?
≥1
≥1
?
≥1
≥1
≥1
?
31
0
27086
0
74983564
536
1.17596026×10¹¹
?
?
?
≥1
?
≥1
≥1
≥1
?
32
0
62872
693134
29476145
250577171
4.05907082×10¹¹
?
?
≥1
≥1
≥1
≥1
≥1
≥1
?
33
0
138902
0
272511
63952
1.27787093×10¹²
?
≥1
?
≥1
?
≥1
≥1
≥1
?
34
0
286826
0
2425794
7.37697093×10¹¹
3.69957005×10¹²
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
35
0
616588
0
2.74707786×10¹⁰
89960
1.26454258×10¹³
?
≥1
?
≥1
?
≥1
≥1
≥1
?
36
0
1359046
21205242
1.15554128×10¹⁰
1.29013455×10¹¹
4.26316755×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
37
0
2972830
0
10873406
4800048
1.36916176×10¹⁴
?
?
?
≥1
?
≥1
≥1
≥1
?
38
0
6298680
0
91199238
3.57263575×10¹³
4.13495679×10¹⁴
?
?
?
≥1
?
≥1
≥1
≥1
?
39
0
13389716
0
9.94553264×10¹¹
8938752
1.33886728×10¹⁵
?
?
?
≥1
?
≥1
≥1
≥1
?
40
0
28785704
624150656
4.40405415×10¹¹
6.41699855×10¹²
4.39268994×10¹⁵
?
?
≥1
≥1
≥1
≥1
≥1
≥1
?
41
0
62040842
0
419778542
296607668
1.41387498×10¹⁶
?
?
?
≥1
?
≥1
≥1
≥1
?
42
0
132096258
0
3.37386361×10¹⁰
1.69713478×10¹⁵
4.37452557×10¹⁶
?
?
≥1
≥1
?
≥1
≥1
≥1
?
43
0
280209316
0
3.56627084×10¹³
691797604
1.38772357×10¹⁷
?
?
?
≥1
?
≥1
≥1
≥1
?
44
0
596047430
1.78860028×10¹¹
1.64419768×10¹³
3.11461289×10¹⁴
4.46334394×10¹⁷
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
45
0
1.27098628×10¹⁰
0
1.58261375×10¹¹
1.65265303×10¹¹
1.42903230×10¹⁸
?
≥1
?
≥1
?
≥1
≥1
≥1
?
46
0
2.69957159×10¹⁰
0
1.23262811×10¹²
7.94306046×10¹⁶
4.47284172×10¹⁸
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
47
0
5.71565778×10¹⁰
0
1.26864976×10¹⁵
4.62601741×10¹¹
1.40896560×10¹⁹
?
≥1
?
≥1
?
≥1
≥1
≥1
?
48
0
1.20974042×10¹¹
5.02593816×10¹²
6.04235715×10¹⁴
1.48436651×10¹⁶
4.47675784×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
49
0
2.56272526×10¹¹
0
5.86060229×10¹²
8.65513091×10¹²
1.42361117×10²⁰
?
?
?
≥1
?
≥1
≥1
≥1
?
50
0
5.42226235×10¹¹
0
4.45825500×10¹³
3.67395655×10¹⁸
≥1.84467440×10²⁰
?
?
≥1
≥1
?
≥1
≥1
≥1
?
51
0
1.14516035×10¹²
0
4.48284873×10¹⁶
2.81361825×10¹³
≥1.84467440×10²⁰
?
?
?
≥1
?
≥1
≥1
≥1
?
52
0
2.41617587×10¹²
1.39120677×10¹⁴
2.19309169×10¹⁶
6.97463251×10¹⁷
≥1.84467440×10²⁰
?
?
≥1
≥1
≥1
≥1
≥1
≥1
?
53
0
5.09748844×10¹²
0
2.14012853×10¹⁴
4.35315000×10¹⁴
≥1.84467440×10²⁰
?
?
?
≥1
?
≥1
≥1
≥1
?
54
0
1.07484149×10¹³
0
1.59913929×10¹⁵
1.68310896×10²⁰
≥1.84467440×10²⁰
?
?
≥1
≥1
?
≥1
≥1
≥1
?
55
0
2.26412174×10¹³
0
1.57498552×10¹⁸
1.60235939×10¹⁵
≥1.84467440×10²⁰
?
≥1
?
≥1
?
≥1
≥1
≥1
?
56
0
4.76519234×10¹³
3.80533916×10¹⁵
7.88020320×10¹⁷
3.24028526×10¹⁹
≥1.84467440×10²⁰
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
57
0
1.00247248×10¹⁴
0
7.72828285×10¹⁵
2.12848515×10¹⁶
≥1.84467440×10²⁰
?
≥1
?
≥1
?
≥1
≥1
≥1
?
58
0
2.10801524×10¹⁴
0
5.69601258×10¹⁶
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
59
0
4.43002628×10¹⁴
0
5.50614644×10¹⁹
8.69844734×10¹⁶
≥1.84467440×10²⁰
?
≥1
?
≥1
?
≥1
≥1
≥1
?
60
0
9.30373168×10¹⁴
1.03084332×10¹⁷
2.80808482×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
61
0
1.95297423×10¹⁵
0
2.76539479×10¹⁷
1.01932323×10¹⁸
≥1.84467440×10²⁰
?
?
?
≥1
?
≥1
≥1
≥1
?
62
0
4.09783238×10¹⁵
0
2.01681453×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
?
≥1
≥1
?
≥1
≥1
≥1
?
63
0
8.59433778×10¹⁵
0
≥1.84467440×10²⁰
4.55379481×10¹⁸
≥1.84467440×10²⁰
?
?
?
≥1
?
≥1
≥1
≥1
?
64
0
1.80159658×10¹⁶
2.77019122×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
?
≥1
≥1
≥1
≥1
≥1
≥1
?
65
0
3.77495729×10¹⁶
0
9.82032558×10¹⁸
4.80434645×10¹⁹
≥1.84467440×10²⁰
?
?
?
≥1
?
≥1
≥1
≥1
?
66
0
7.90674781×10¹⁶
0
7.10437906×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
67
0
1.65545707×10¹⁷
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
?
≥1
?
≥1
≥1
≥1
?
68
0
3.46471767×10¹⁷
7.39425205×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
69
0
7.24861339×10¹⁷
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
?
≥1
?
≥1
≥1
≥1
?
70
0
1.51597263×10¹⁸
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
71
0
3.16944976×10¹⁸
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
?
≥1
?
≥1
≥1
≥1
?
72
0
6.62420589×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
73
0
1.38402801×10¹⁹
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
?
?
≥1
?
≥1
≥1
≥1
?
74
0
2.89083773×10¹⁹
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
?
≥1
≥1
?
≥1
≥1
≥1
?
75
0
6.03637440×10¹⁹
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
?
?
≥1
?
≥1
≥1
≥1
?
76
0
1.26010150×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
?
≥1
≥1
≥1
≥1
≥1
≥1
?
77
0
2.62975253×10²⁰
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
?
≥1
?
≥1
≥1
≥1
?
78
0
5.48666476×10²⁰
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
79
0
1.14443344×10²¹
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
?
≥1
?
≥1
≥1
≥1
?
80
0
2.38651761×10²¹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
81
0
4.97546474×10²¹
?
≥1
≥1
≥1
?
≥1
?
≥1
?
≥1
≥1
≥1
?
82
0
1.03705239×10²²
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
83
0
2.16107122×10²²
?
≥1
≥1
≥1
?
≥1
?
≥1
?
≥1
≥1
≥1
?
84
0
4.50237640×10²²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
85
0
9.37824339×10²²
?
≥1
≥1
≥1
?
?
?
≥1
?
≥1
≥1
≥1
?
86
0
1.95303831×10²³
?
≥1
≥1
≥1
?
?
≥1
≥1
?
≥1
≥1
≥1
?
87
0
4.06641976×10²³
?
≥1
≥1
≥1
?
?
?
≥1
?
≥1
≥1
≥1
?
88
0
8.46502686×10²³
≥1
≥1
≥1
≥1
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
89
0
1.76181978×10²⁴
?
≥1
≥1
≥1
?
≥1
?
≥1
?
≥1
≥1
≥1
?
90
0
3.66618043×10²⁴
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
91
0
7.62759392×10²⁴
?
≥1
≥1
≥1
?
≥1
?
≥1
?
≥1
≥1
≥1
?
92
0
1.58666328×10²⁵
≥1
≥1
≥1
≥1
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
93
0
3.29995070×10²⁵
?
≥1
≥1
≥1
?
≥1
?
≥1
?
≥1
≥1
≥1
?
94
0
6.86210727×10²⁵
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
≥1
≥1
≥1
?
95
0
1.42671347×10²⁶
?
≥1
≥1
≥1
?
≥1
?
≥1
?
≥1
≥1
≥1
?
96
0
2.96583519×10²⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
97
0
6.16438806×10²⁶
?
≥1
≥1
≥1
?
?
?
≥1
?
≥1
≥1
≥1
?
98
0
1.28105350×10²⁷
?
≥1
≥1
≥1
?
?
≥1
≥1
?
≥1
≥1
≥1
?
99
0
2.66183110×10²⁷
?
≥1
≥1
≥1
?
≥1
?
≥1
?
≥1
≥1
≥1
?
100
0
5.53007698×10²⁷
≥1
≥1
≥1
≥1
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
all
?
?
?
?
?
?
?
?
?
?
?
?

See Also

I tetromino and X2 hexominoI tetromino and U heptomino