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 X2 hexomino

Prime rectangles: ≥ 6.

Smallest rectangle tilings

Smallest known rectangle (13x24):

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
15
N>0
1-12
0
13
0
0
14
0
0
0
15
0
0
0
0
16
0
0
0
0
?
17
0
0
0
?
?
18
0
0
?
?
?
19
0
0
?
?
?
20
0
0
?
?
?
21
0
0
?
?
?
22
0
0
?
?
?
23
0
0
?
?
?
24
0
50
?
?
?
25
0
0
?
?
?
26
0
0
?
?
?
27
0
0
?
?
?
28
0
20020
?
?
?
29
0
0
?
?
?
30
0
0
?
?
?
31
0
0
?
?
?
32
0
4591428
?
?
?
33
0
0
?
?
?
34
0
0
?
?
?
35
0
0
?
?
?
36
0
830263398
?
?
?
37
0
0
?
?
?
38
0
0
?
?
?
39
0
0
?
?
?
40
0
1.33826117×10¹²
?
?
?
41
0
0
?
?
?
42
0
0
?
?
?
43
0
0
?
?
?
44
0
2.02900140×10¹⁴
?
?
?
45
0
0
?
?
?
46
0
0
?
?
?
47
0
0
?
?
?
48
0
2.96621758×10¹⁶
?
?
?
49
0
0
?
?
?
50
0
0
?
?
?
51
0
0
?
?
?
52
0
4.23231835×10¹⁸
?
?
?
53
0
0
?
?
?
54
0
0
?
?
?
55
0
0
?
?
?
56
0
≥1.84467440×10²⁰
?
?
?
N>0
x
?
?
?

See Also

I tetromino and T1 hexominoI tetromino and C heptomino