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 triomino and O tetromino

Prime rectangles: 10.

Smallest rectangle tilings

Smallest rectangle (2x5):

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
0
5
5
0
4
0
16
0
6
0
0
0
18
64
382
7
0
6
0
92
0
1856
5504
8
0
12
0
244
1128
9019
71248
652035
9
0
8
0
472
0
42512
231296
4937224
≥1
10
0
24
0
1425
8120
199683
≥1
≥1
≥1
≥1
11
0
42
0
3720
6912
922464
≥1
≥1
≥1
≥1
≥1
12
0
40
0
8600
52360
4256362
≥1
≥1
≥1
≥1
≥1
≥1
13
0
92
0
22808
75136
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
0
140
0
58176
491960
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
174
0
142988
643840
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
≥1
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
≥1
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
≥1
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
≥1
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
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
all
all
all
all
all
all
all
all
all
all
all
?
?
?
?
?

See Also

L triomino and L tetrominoL triomino and T tetromino