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.


L tetromino and O tetromino

Prime rectangles: 6.

Smallest rectangle tilings

Smallest rectangles (2x6, 3x4):

Smallest square (4x4):

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
6
8
5
0
0
0
48
0
6
0
4
0
98
0
≥1000
7
0
0
0
378
0
0
0
8
0
6
44
880
≥1000
≥1000
≥1000
≥1000
9
0
0
0
≥1000
0
0
0
≥1000
0
10
0
20
0
≥1000
0
≥1000
0
≥1000
0
≥1
11
0
0
0
≥1000
0
0
0
≥1
0
0
0
12
0
34
384
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
0
0
≥1000
0
0
0
≥1
0
0
0
≥1
0
14
0
84
0
≥1000
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
15
0
0
0
≥1000
0
0
0
≥1
0
0
0
≥1
0
0
0
16
0
154
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
0
0
≥1000
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
0
18
0
340
0
≥1000
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
19
0
0
0
≥1000
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
0
0
0
20
0
650
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
2k
4k
all
4k
2k
4k
all
4k
2k
4k
all
4k
2k
4k
all
4k
2k
4k
all

See Also

I tetromino and U heptominoL tetromino and T tetromino