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.


I tetromino and Z tetromino

Prime rectangles: ≥ 9.

Smallest rectangle tilings

Smallest rectangle (5x8):

Smallest square (8x8):

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
1-2
0
3
0
0
4
0
0
0
5
0
0
0
0
6
0
0
0
0
0
7
0
0
0
0
0
0
8
0
0
0
6
30
118
540
9
0
0
0
0
0
0
1770
0
10
0
0
0
0
0
0
8646
0
0
11
0
0
0
0
0
0
39826
0
0
0
12
0
0
0
90
1503
16220
171293
≥1000
≥1000
≥1
≥1
13
0
0
0
0
0
0
594542
0
0
0
≥1
0
14
0
0
0
0
0
0
2416579
0
?
0
≥1
0
?
15
0
0
0
0
0
0
10226880
0
?
0
≥1
0
?
0
16
0
0
0
964
62825
1677828
≥23400000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
?
?
0
?
0
≥1
0
?
0
≥1
0
?
0
≥1
?
18
0
?
?
0
?
0
≥1
0
?
0
≥1
0
?
0
≥1
?
?
19
0
?
?
0
?
0
≥1
0
?
0
≥1
0
?
0
≥1
?
?
?
20
0
?
?
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
?
?
4k
?
4k
all
4k
?
4k
all
4k
?
4k
all
?
?
?
?

See Also

I tetromino and T tetrominoI tetromino and I pentomino