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.


Z tetromino and L pentomino

Prime rectangles: ≥ 18.

Smallest rectangle tilings

Smallest known rectangle (3x6):

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
0
0
0
0
6
0
0
2
0
2
8
7
0
0
0
6
0
14
0
8
0
0
0
0
8
124
192
728
9
0
0
0
16
0
126
380
≥1000
≥1000
10
0
0
0
0
24
220
≥1000
≥1000
≥1000
≥1000
11
0
0
0
8
4
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
12
0
0
4
48
150
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
13
0
0
0
8
120
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
14
0
0
0
180
842
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
15
0
0
0
26
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
16
?
?
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
?
?
?
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
?
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
?
?
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
?
?
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1

See Also

Z tetromino and I pentominoZ tetromino and P pentomino