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.


T tetromino and I pentomino

Prime rectangles: ≥ 36.

Smallest rectangle tilings

Smallest known rectangles and smallest square (4x9, 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
N>0
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
4
7
0
0
0
0
0
6
6
8
0
0
0
0
0
12
12
24
9
0
0
0
12
0
34
13
452
≥1000
10
0
0
0
0
18
90
168
≥1000
≥1000
≥1000
11
0
0
0
2
40
180
407
≥1000
≥1000
≥1000
≥1000
12
0
0
0
0
62
246
508
≥1000
≥1000
≥1000
≥1000
≥1000
13
0
0
0
86
84
788
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
14
0
0
2
40
138
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
15
0
0
0
22
568
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
16
0
0
0
14
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
17
0
0
2
444
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
18
0
0
0
586
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
19
0
0
18
232
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
20
0
0
2
284
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
?
?
?
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

See Also

T tetromino and Z tetrominoT tetromino and L pentomino