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 O hexomino

Prime rectangles: 7.

Smallest rectangle tilings

Smallest rectangle (2x5):

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
2
0
4
0
6
0
0
0
2
8
12
7
0
3
0
9
0
45
0
8
0
3
0
15
26
89
280
818
9
0
4
0
24
0
226
0
2670
0
10
0
6
0
48
66
546
1511
8254
≥10000
≥10000
11
0
9
0
81
0
1243
0
≥10000
0
≥10000
0
12
0
10
0
142
162
3036
7937
≥10000
≥10000
≥10000
≥10000
≥10000
13
0
16
0
256
0
7056
0
≥10000
0
≥10000
0
≥10000
0
14
0
20
0
440
418
≥10000
≥10000
≥10000
≥10000
≥10000
≥10000
≥10000
≥1
≥1
15
0
27
0
783
0
≥10000
0
≥10000
0
≥10000
0
≥10000
0
≥1
0
16
0
36
0
1368
1054
≥10000
≥10000
≥10000
≥10000
≥10000
≥10000
≥10000
≥1
≥1
≥1
≥1
17
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
18
0
≥1
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
20
0
≥1
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
all
x
all
2k
all
2k
all
2k
all
2k
all
2k
all
2k
all
?
?
?
?

See Also

O tetromino and L hexominoO tetromino and P hexomino