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 T pentomino

Prime rectangles: 21.

Smallest rectangle tilings

Smallest rectangle and 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
1-3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1-3
0
4
0
4
5
0
0
0
6
0
0
0
0
7
0
32
16
28
1086
8
0
16
0
64
2002
832
9
0
0
20
164
3082
10904
62728
10
0
202
252
918
33564
131912
558682
≥1
11
0
208
28
2358
≥1
≥1
≥1
≥1
≥1
12
0
64
488
6292
≥1
≥1
≥1
≥1
≥1
≥1
13
0
1154
2768
22256
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
0
1808
862
59700
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
1152
7002
160276
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
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all
all
all
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See Also

I triomino and R pentominoI triomino and U pentomino