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 N pentomino

Prime rectangles: ≥ 35.

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
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
0
0
8
0
0
0
0
0
0
68
0
9
0
0
0
8
0
8
52
392
408
10
0
0
0
0
0
0
170
≥1000
≥1000
≥1000
11
0
0
0
12
0
8
328
≥1000
≥1000
≥1000
≥1000
12
0
0
0
0
20
58
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
13
0
0
0
100
60
68
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
14
0
0
0
18
50
50
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
15
0
0
0
134
68
450
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
16
0
0
0
80
88
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
17
0
0
0
592
360
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
18
0
0
0
730
826
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
19
0
0
0
792
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
20
0
0
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1

See Also

T tetromino and L pentominoT tetromino and P pentomino