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.


N pentomino, T pentomino and X pentomino

Prime rectangles: ≥ 38.

Smallest rectangle tilings

Smallest known rectangle (5x14):

Smallest square (10x10):

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
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1
0
2
0
0
3
0
0
0
4
0
0
0
0
5
0
0
0
0
0
6
0
0
0
0
0
0
7
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
≥1
≥1
11
0
0
0
0
0
0
0
0
0
≥1
0
12
0
0
0
0
0
0
0
0
0
≥1
0
0
13
0
0
0
0
0
0
0
0
0
≥1
0
0
0
14
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
15
0
0
0
0
0
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
0
0
0
0
0
0
0
0
≥1
0
0
0
0
≥1
0
17
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
18
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
19
0
0
0
0
0
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
20
0
0
0
0
≥1
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
22
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
23
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
24
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
25
0
0
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
26
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
27
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
28
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
29
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
30
0
0
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
31
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
32
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
33
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
34
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
35
0
0
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
36
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
37
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
38
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
39
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
40
0
0
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
41
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
42
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
43
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
44
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
45
0
0
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
46
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
47
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
48
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
49
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
?
≥1
50
0
0
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1

See Also

I tetromino, X pentomino and Z pentominoU octomino, A1 9-omino and T1 10-omino