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.


O tetromino and L pentomino

Prime rectangles: ≥ 17.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (6x6):

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
2
0
4
22
7
0
4
0
16
0
78
0
8
0
0
0
5
18
202
438
1390
9
0
6
0
36
0
372
296
5906
≥1
10
0
0
0
18
64
952
3192
21762
≥1
≥1
11
0
8
0
64
16
2410
5068
91866
≥1
≥1
≥1
12
0
12
4
185
300
6582
31116
353954
≥1
≥1
≥1
≥1
13
0
10
0
172
192
17214
63320
1303970
≥1
≥1
≥1
≥1
≥1
14
0
24
0
682
1010
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
12
0
648
1040
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
40
0
1868
3290
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
46
0
2972
4312
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
60
8
4951
13950
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
?
≥1
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
?
≥1
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1

See Also

O tetromino and I pentominoO tetromino and N pentomino