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.


O tetromino and I pentomino

Prime rectangles: ≥ 23.

Smallest rectangle tilings

Smallest rectangle (2x7):

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
0
0
0
2
7
0
2
0
4
0
12
28
8
0
0
0
0
0
6
36
26
9
0
3
0
9
0
33
108
137
838
10
0
0
2
3
7
21
140
348
1185
4876
11
0
4
0
16
14
104
490
846
5856
15387
≥1
12
0
3
0
17
21
165
950
2083
13094
49459
≥1
≥1
13
0
5
0
25
28
263
1948
3769
37522
139640
≥1
≥1
≥1
14
0
6
0
51
35
625
4154
10423
109950
424612
≥1
≥1
≥1
≥1
15
0
6
12
54
174
918
8962
33144
287424
1740947
≥1
≥1
≥1
≥1
≥1
16
0
10
0
124
327
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
11
0
139
494
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
15
0
260
675
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
18
0
364
870
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
21
46
559
2727
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1

Smallest prime reptiles

Smallest prime reptiles (4Ox3, 5Ix3):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
O tetromino
?
?
?
?
?
I pentomino
?
?
?
?
?

See Also

O tetromino and T tetrominoO tetromino and L pentomino