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 triomino and U pentomino

Prime rectangles: 26.

Smallest rectangle tilings

Smallest rectangle (4x7):

Smallest square (7x7):

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
1-3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1-3
0
4
0
0
5
0
0
0
6
0
0
0
0
7
0
2
2
0
98
8
0
0
2
18
122
410
9
0
0
8
62
262
2600
16136
10
0
22
40
144
3582
12276
70186
585068
11
0
4
30
650
≥1
≥1
≥1
≥1
≥1
12
0
0
130
1996
≥1
≥1
≥1
≥1
≥1
≥1
13
0
162
462
5054
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
0
54
362
15968
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
8
1456
45294
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
1008
4386
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
480
3886
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
132
13966
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
5748
38022
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
3540
38428
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
all
all
all
all
all
all
all
all
all
all
all
all
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See Also

I triomino and T pentominoI triomino and V pentomino