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 B hexomino

Prime rectangles: ≥ 22.

Smallest rectangle tilings

Smallest rectangle (6x10):

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
1-5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-5
0
6
0
0
7
0
0
0
8
0
0
0
0
9
0
0
0
18
0
10
0
9
0
18
0
54
11
0
0
0
54
0
0
0
12
0
27
0
270
328
1710
4192
14684
13
0
0
0
360
0
0
0
74624
0
14
0
72
0
1584
0
18286
0
306441
0
≥1
15
0
0
0
2376
0
0
0
998798
0
?
?
16
0
279
216
6894
10222
145782
366016
4562498
≥1900000
≥1
≥1
≥1
17
0
0
0
18738
?
?
?
≥1
?
?
?
≥1
?
18
0
882
0
≥1000
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
19
0
0
0
≥1000
?
?
?
≥1
?
?
?
≥1
?
?
?
20
0
≥1000
1520
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
0
≥1000
?
?
?
≥1
?
?
?
≥1
?
?
?
≥1
?
22
0
≥1000
0
≥1000
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
23
0
0
0
≥1000
?
?
?
≥1
?
?
?
≥1
?
?
?
≥1
?
24
0
≥1000
23808
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
25
0
0
0
≥1000
?
?
?
≥1
?
?
?
≥1
?
?
?
≥1
?
26
0
≥1000
0
≥1000
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
27
0
0
0
≥1000
?
?
?
≥1
?
?
?
≥1
?
?
?
≥1
?
28
0
≥1000
308504
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
29
0
0
0
≥1000
?
?
?
≥1
?
?
?
≥1
?
?
?
≥1
?
30
0
≥1000
0
≥1000
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
31
0
0
0
≥1000
?
?
?
≥1
?
?
?
≥1
?
?
?
≥1
?
32
0
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
?
?
all
?
?
?
all
?
?
?
?
?
?
?
?

See Also

O tetromino and A hexominoO tetromino and C hexomino