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 pentomino and R pentomino

Prime rectangles: ≥ 28.

Smallest rectangle tilings

Smallest known rectangle (10x11):

Smallest square (15x15):

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
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
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
0
0
11
0
0
0
0
0
0
0
0
0
2
0
12
0
0
0
0
0
0
0
0
0
10
0
0
13
0
0
0
0
0
0
0
0
0
18
0
0
0
14
0
0
0
0
0
0
0
0
0
30
0
0
0
0
15
0
0
0
0
0
0
0
0
0
42
770
≥1000
≥1000
≥1000
≥1000
16
0
0
0
0
0
0
0
0
0
202
0
0
0
0
≥1000
?
17
0
0
0
0
0
0
0
0
0
878
0
0
0
0
≥1000
?
?
18
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
0
≥1000
?
?
?
19
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
0
≥1000
?
?
?
?
20
0
0
0
0
0
2
6
68
334
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
21
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
0
≥1000
?
?
?
?
≥1
22
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
0
≥1000
?
?
?
?
≥1
23
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
0
≥1000
?
?
?
?
≥1
24
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
0
≥1000
?
?
?
?
≥1
25
0
0
0
0
0
44
214
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1

See Also

I pentomino and P pentominoI pentomino and T pentomino