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 hexomino

Prime rectangles: 26.

Smallest rectangle tilings

Smallest rectangle (7x10):

Smallest square (10x10):

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
1-6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-6
0
7
0
0
8
0
0
0
9
0
0
4
0
10
0
4
10
6
12
11
0
0
16
0
246
0
12
0
2
26
300
853
1922
7180
13
0
0
110
0
438
0
45730
0
14
0
68
306
312
878
25960
157988
130078
≥1
15
0
0
624
0
11336
0
420214
0
≥1
0
16
0
40
1170
12614
45228
147078
≥1
≥1
≥1
≥1
≥1
17
0
0
2932
0
22756
0
≥1
0
≥1
0
≥1
0
18
0
796
7406
11642
48212
1856660
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
16414
0
483516
0
≥1
0
≥1
0
≥1
0
≥1
0
20
0
538
33610
434170
2047040
9558338
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
74196
0
1038310
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
22
0
8054
170920
387568
2302089
113554220
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
23
0
0
380576
0
19784414
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
24
0
6110
809760
13736002
86144665
569760130
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
25
0
0
1740718
0
44344348
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
26
0
75514
3824560
12168986
101370342
6.40688119×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
27
0
0
8377280
0
785766810
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
28
0
63216
17995990
415446396
3.47016487×10¹⁰
3.21628243×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
29
0
0
38493090
0
1.81883989×10¹⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
30
0
675846
82887692
368219796
4.24677934×10¹⁰
3.44491117×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
31
0
0
178871078
0
3.05239009×10¹¹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
32
0
616764
383420242
1.22004037×10¹¹
1.35670769×10¹²
1.74939078×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
33
0
0
818056820
0
7.25588342×10¹¹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
34
0
5863504
1.74623032×10¹⁰
1.08579031×10¹¹
1.72109441×10¹²
1.79464327×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
35
0
0
3.73212936×10¹⁰
0
1.16596654×10¹³
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
36
0
5779458
7.96012569×10¹⁰
3.50689801×10¹²
5.19020162×10¹³
9.26456098×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
37
0
0
1.69307363×10¹¹
0
2.83614389×10¹³
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
38
0
49758174
3.59702498×10¹¹
3.14105365×10¹²
6.81171150×10¹³
9.14510237×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
39
0
0
7.64229547×10¹¹
0
4.39575126×10¹⁴
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
40
0
52583268
1.62243674×10¹²
9.91665829×10¹³
1.95317712×10¹⁵
4.80927565×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
41
0
0
3.43935148×10¹²
0
1.09139518×10¹⁵
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
42
0
415379086
7.28255208×10¹²
8.95351642×10¹³
2.64826844×10¹⁵
4.58577610×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
43
0
0
1.54123157×10¹³
0
1.63986951×10¹⁶
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
44
0
467757122
3.26000765×10¹³
2.76835444×10¹⁵
7.25641297×10¹⁶
2.45820998×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
45
0
0
6.88978758×10¹³
0
4.14836093×10¹⁶
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
46
0
3.42420443×10¹⁰
1.45483504×10¹⁴
2.52240860×10¹⁵
1.01535899×10¹⁷
2.27189314×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
47
0
0
3.07010332×10¹⁴
0
6.06510904×10¹⁷
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
48
0
4.08751586×10¹⁰
6.47547832×10¹⁴
7.64860598×10¹⁶
2.66829162×10¹⁸
1.24117043×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
49
0
0
1.36501975×10¹⁵
0
1.56110319×10¹⁸
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
50
0
2.79496854×10¹¹
2.87560240×10¹⁵
7.03865836×10¹⁶
3.84964222×10¹⁸
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
51
0
0
6.05446670×10¹⁵
0
2.22711304×10¹⁹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
52
0
3.52069579×10¹¹
1.27413772×10¹⁶
2.09531983×10¹⁸
9.72945831×10¹⁹
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
53
0
0
2.68011991×10¹⁶
0
5.82641873×10¹⁹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
54
0
2.26332160×10¹²
5.63480775×10¹⁶
1.94860699×10¹⁸
1.44621544×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
55
0
0
1.18413258×10¹⁷
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
56
0
2.99647311×10¹²
2.48735190×10¹⁷
5.69945116×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
57
0
0
5.22276467×10¹⁷
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
58
0
1.82097876×10¹³
1.09620067×10¹⁸
5.35869916×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
59
0
0
2.29990468×10¹⁸
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
60
0
2.52482071×10¹³
4.82357973×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
61
0
0
1.01129498×10¹⁹
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
62
0
1.45727669×10¹⁴
2.11952709×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
63
0
0
4.44074854×10¹⁹
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
64
0
2.10927841×10¹⁴
9.30111502×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
65
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
66
0
1.16102339×10¹⁵
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
67
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
68
0
1.74918120×10¹⁵
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
69
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
70
0
9.21524948×10¹⁵
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
71
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
72
0
1.44128721×10¹⁶
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
73
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
74
0
7.29100131×10¹⁶
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
75
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
76
0
1.18093150×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
77
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
78
0
5.75285062×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
79
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
80
0
9.62817231×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
81
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
82
0
4.52857715×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
83
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
84
0
7.81537006×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
85
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
86
0
3.55764368×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
87
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
88
0
6.31898668×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
89
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
90
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
91
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
92
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
93
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
94
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
95
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
96
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
97
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
98
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
99
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
100
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
2k
all
2k
all
2k
all
2k
all
?
?
?
?
?
?

See Also

I tetromino and A hexominoI tetromino and G hexomino