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 Y pentomino

Prime rectangles: 27.

Smallest rectangle tilings

Smallest rectangle (4x8):

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
0
0
48
68
8
0
8
24
96
1604
12352
9
0
28
70
256
14228
98194
441692
10
0
0
124
2418
19848
≥1
≥1
≥1
11
0
112
834
9152
196986
≥1
≥1
≥1
≥1
12
0
538
4066
26166
1584484
≥1
≥1
≥1
≥1
≥1
13
0
98
9888
106414
3685952
≥1
≥1
≥1
≥1
≥1
≥1
14
0
952
17672
461580
18489144
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
5772
132238
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
3458
326806
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
9002
300548
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
49050
2644246
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
51444
6947130
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
106090
5665062
≥1
≥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
all
all
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all
all

See Also

I triomino and X pentominoI triomino and Z pentomino