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.


U pentomino and I hexomino

Prime rectangles: ≥ 5.

Smallest rectangle tilings

Smallest known rectangle (14x24):

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
1-12
13
14
N>0
1-12
0
13
0
0
14
0
0
?
15
0
0
?
?
16
0
0
?
?
17
0
0
?
?
18
0
0
?
?
19
0
0
?
?
20
0
0
?
?
21
0
0
?
?
22
0
0
?
?
23
0
0
?
?
24
0
0
≥1
?
25
0
0
?
?
26
0
0
?
?
27
0
0
?
?
28
0
0
?
?
29
0
0
?
?
30
0
0
?
?
31
0
0
?
?
32
0
0
?
?
33
0
0
?
?
34
0
0
?
?
35
0
0
?
?
36
0
0
?
?
37
0
0
?
?
38
0
0
?
?
39
0
0
?
?
40
0
0
?
?
41
0
0
?
?
42
0
0
?
?
43
0
0
?
?
44
0
0
?
?
45
0
0
?
?
46
0
0
?
?
47
0
0
?
?
48
0
0
≥1
?
49
0
0
?
?
50
0
0
?
?
51
0
0
?
?
52
0
0
?
?
53
0
0
?
?
54
0
200
?
?
55
0
0
?
?
56
0
0
?
?
57
0
0
?
?
58
0
0
?
?
59
0
0
?
?
60
0
31920
?
?
61
0
0
?
?
62
0
0
?
?
63
0
0
?
?
64
0
0
?
?
65
0
0
?
?
66
0
2907408
?
?
67
0
0
?
?
68
0
0
?
?
69
0
0
?
?
70
0
0
?
?
71
0
0
?
?
72
0
200670362
≥1
?
N>0
x
?
?

See Also

U pentomino and F hexominoU pentomino and J hexomino