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.


V pentomino and C hexomino

Prime rectangles: ≥ 27.

Smallest rectangle tilings

Smallest rectangle (8x19):

Smallest square (22x22):

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
9-13
14
15
16
17
18
19
20
21
22
N>0
1-7
0
8
0
0
9-13
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
2
0
0
0
4
0
0
0
20
0
0
0
0
0
0
0
0
0
0
21
0
0
0
0
0
0
0
0
0
?
0
22
0
0
0
0
0
6
0
0
0
?
?
2
23
0
0
0
0
0
0
0
0
0
?
?
?
?
24
0
0
0
0
0
0
0
0
8
?
?
?
?
25
0
0
0
0
0
0
0
0
0
?
?
?
?
26
0
0
0
0
0
0
0
2
0
?
?
?
?
27
0
0
0
0
0
0
0
0
0
?
?
?
?
28
0
0
0
0
0
0
0
0
2
?
?
?
?
29
0
0
0
0
0
0
0
0
0
?
?
?
?
30
0
0
0
0
0
0
0
0
0
?
?
?
?
31
0
0
0
0
0
0
0
0
0
?
?
?
?
32
0
0
0
0
0
0
0
0
16
?
?
≥1
?
33
0
0
0
0
0
0
0
0
0
?
?
?
?
34
0
0
0
0
0
0
0
0
0
?
?
?
?
35
0
0
0
0
0
0
0
0
0
?
?
?
?
36
0
0
0
2
0
0
0
0
8
?
?
?
?
37
0
0
0
0
0
0
0
0
4
?
?
?
?
38
0
4
0
0
0
16
4
0
0
?
?
≥1
?
39
0
0
0
0
0
0
0
0
?
?
?
?
?
40
0
0
0
0
0
32
0
0
≥1
?
?
?
?
41
0
0
0
0
0
48
0
0
?
?
?
?
?
42
0
0
0
0
0
0
0
0
?
?
?
?
?
43
0
0
0
0
0
32
0
0
?
?
?
?
?
44
0
0
0
2
0
44
0
2
≥1
?
?
≥1
?
45
0
0
0
0
0
32
0
0
≥1
?
?
?
?
46
0
0
0
0
0
14
0
0
?
?
?
?
?
47
0
0
0
0
0
0
0
0
?
?
?
?
?
48
0
0
0
0
0
20
0
0
≥1
?
?
≥1
?
49
0
0
0
0
0
0
0
2
?
?
?
?
?
50
0
0
0
0
0
26
0
0
?
?
?
?
?
51
0
0
0
0
0
16
0
8
?
?
?
?
?
52
0
0
0
0
0
0
0
4
≥1
?
?
?
?
53
0
0
0
0
0
0
0
0
≥1
?
?
?
?
54
0
0
0
0
0
12
0
6
?
?
?
≥1
?
55
0
0
0
0
0
0
0
0
?
?
?
?
?
56
0
0
0
0
0
52
0
?
≥1
?
?
?
?
57
0
8
0
0
0
96
0
?
?
?
?
?
?
58
0
0
0
0
0
8
0
?
?
?
?
?
?
59
0
0
0
0
0
264
0
?
?
?
?
?
?
60
0
0
0
0
0
312
?
?
≥1
?
?
≥1
?
61
0
0
0
0
0
512
?
?
≥1
?
?
?
?
62
0
0
0
0
0
≥1
?
?
?
?
?
?
?
63
0
0
0
0
0
≥1
?
?
?
?
?
?
?
64
0
0
0
0
0
≥1
?
?
≥1
?
?
≥1
?
65
0
0
0
0
0
≥1
?
?
≥1
?
?
?
?
66
0
0
0
0
0
≥1
?
?
?
?
?
≥1
?
67
0
0
0
0
0
≥1
?
?
?
?
?
?
?
68
0
0
0
0
0
≥1
?
?
≥1
?
?
?
?
69
0
0
0
0
0
≥1
?
?
≥1
?
?
?
?
70
0
0
0
0
0
≥1
?
≥1
?
?
?
≥1
?
71
0
0
0
0
0
≥8
?
?
?
?
?
?
?
72
0
0
0
6
0
≥1
?
?
≥1
?
?
?
?
73
0
0
0
0
0
≥1
?
?
≥1
?
?
?
?
74
0
0
0
0
0
≥2
?
?
≥1
?
?
?
?
75
0
0
0
0
0
≥1
?
≥1
?
?
?
?
?
76
0
16
0
0
0
≥1
≥1
?
≥1
?
?
≥1
?
77
0
0
0
0
0
≥1
?
≥1
≥1
?
?
?
?
78
0
0
0
0
2
≥1
?
≥1
?
?
?
?
?
79
0
0
0
0
0
≥1
?
?
?
?
?
?
?
80
0
0
0
8
0
≥1
?
≥1
≥1
?
?
≥1
?
N>0
x
?
x
?
?
all
?
?
?
?
?
?

See Also

V pentomino and B hexominoV pentomino and D hexomino