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.


T pentomino and U pentomino

Prime rectangles: ≥ 79.

Smallest rectangle tilings

Smallest rectangle (13x25):

Smallest 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
1-11
12
13
14
15
16
17
18
19
20
21
22
N>0
1-11
0
12
0
0
13
0
0
0
14
0
0
0
0
15
0
0
0
0
0
16
0
0
0
0
0
0
17
0
0
0
0
0
0
0
18
0
0
0
0
0
0
0
0
19
0
0
0
0
0
0
0
0
0
20
0
0
0
0
0
0
≥1
≥1
0
≥1
21
0
0
0
0
0
0
0
0
0
≥1
0
22
0
0
0
0
0
0
0
0
0
≥1
0
0
23
0
0
0
0
0
0
0
0
0
≥1
0
0
5k
24
0
0
0
0
≥1
0
0
0
0
≥1
0
0
5k
25
0
0
2
0
0
0
≥1
≥1
≥1
≥1
≥1
≥1
all
26
0
0
0
0
0
0
0
0
0
≥1
0
0
?
27
0
0
0
0
0
0
0
0
0
≥1
0
0
?
28
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
29
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
30
0
2
34
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
31
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
32
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
33
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
34
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
35
0
0
68
8
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
?
36
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
37
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
38
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
39
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
40
0
10
656
40
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
41
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
42
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
43
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
44
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
45
0
14
3354
568
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
46
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
47
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
48
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
49
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
50
0
104
26134
4130
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
51
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
52
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
53
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
54
0
0
0
0
?
0
0
0
0
≥1
0
0
?
55
0
344
170644
41812
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
56
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
57
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
58
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
59
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
60
0
1632
1215238
352476
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
61
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
62
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
63
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
64
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
65
0
6054
8234312
3396650
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
66
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
67
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
68
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
69
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
70
0
27864
57339232
31167464
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
71
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
72
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
73
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
74
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
75
0
112518
392710870
297022614
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
76
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
77
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
78
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
79
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
80
0
533096
2.71482101×10¹⁰
2.79638830×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
81
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
82
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
83
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
84
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
85
0
2246660
1.86615649×10¹¹
2.65830770×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
86
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
87
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
88
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
89
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
90
0
10673400
1.28691690×10¹²
2.52011047×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
91
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
92
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
93
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
94
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
95
0
46699166
8.85776708×10¹²
2.39425986×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
96
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
97
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
98
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
99
0
0
0
0
≥1
0
0
0
0
≥1
0
0
?
100
0
219143978
6.10363213×10¹³
2.27377914×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
5k
5k
5k
all
5k
5k
5k
5k
all
5k
5k

See Also

R pentomino and Y2 hexominoT pentomino and W pentomino