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.


Z pentomino and I hexomino

Prime rectangles: ≥ 36.

Smallest rectangle tilings

Smallest rectangle (12x13):

Smallest square (18x18):

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
1-8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-8
0
9
0
0
10
0
0
0
11
0
0
0
0
12
0
0
0
0
0
13
0
0
0
0
2
0
14
0
0
0
0
4
0
0
15
0
0
0
0
6
0
0
0
16
0
0
0
0
8
0
0
0
0
17
0
0
0
0
10
0
0
0
0
0
18
0
0
0
0
12
308
≥1
≥1
≥1
≥1
≥100
19
0
0
0
0
156
0
0
0
0
?
≥1
?
20
0
0
0
0
343
0
0
0
0
?
≥1
?
?
21
0
0
0
0
578
0
0
0
0
?
≥1
?
?
?
22
0
0
0
0
869
0
0
0
0
?
≥1
?
?
?
23
0
0
0
0
1224
0
0
0
?
?
≥1
?
?
?
24
0
2
4
6
1659
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
25
0
0
0
0
≥5000
0
?
?
?
?
≥1
?
?
?
26
0
0
0
0
≥5000
0
?
?
?
?
≥1
?
?
?
27
0
0
0
0
≥5000
0
0
?
?
?
≥1
?
?
?
28
0
0
0
0
≥5000
?
?
?
?
?
≥1
?
?
?
29
0
0
0
0
≥5000
?
?
?
?
?
≥1
?
?
?
30
0
62
132
210
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
31
0
0
0
0
≥5000
?
?
?
?
?
≥1
?
?
?
32
0
0
0
0
≥5000
?
?
?
?
?
≥1
?
?
?
33
0
0
0
0
≥5000
?
?
?
?
?
≥1
?
?
?
34
0
0
0
0
≥5000
?
?
?
?
?
≥1
?
?
?
35
0
0
0
0
≥5000
?
?
?
?
?
≥1
?
?
?
36
0
1112
2564
4392
≥5000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
37
0
0
0
?
≥1
?
?
?
?
?
≥1
?
?
?
38
0
0
0
?
≥1
?
?
?
?
?
≥1
?
?
?
39
0
0
0
?
≥1
?
?
?
?
?
≥1
?
?
?
40
0
0
0
?
≥1
?
?
?
?
?
≥1
?
?
?
41
0
0
?
?
≥1
?
?
?
?
?
≥1
?
?
?
42
0
≥100
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
43
0
0
?
?
≥1
?
?
?
?
?
≥1
?
?
?
44
0
0
?
?
≥1
?
?
?
?
?
≥1
?
?
?
45
0
0
?
?
≥1
?
?
?
?
?
≥1
?
?
?
46
0
0
?
?
≥1
?
?
?
?
?
≥1
?
?
?
47
0
0
?
?
≥1
?
?
?
?
?
≥1
?
?
?
48
0
≥100
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
?
?
?
?
?
?
?
?
?
?
?
?

See Also

Z pentomino and G hexominoZ pentomino and J hexomino