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.


Dominoes and I pentomino

Prime rectangles: 15.

Smallest rectangle tilings

Smallest rectangle (1x7):

Smallest square (5x5):

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
16
24
572
6
0
2
6
78
1451
9576
7
2
7
138
617
15000
106161
≥1
8
0
14
76
2034
50640
681596
≥1
≥1
9
3
32
847
9604
360302
5875580
≥1
≥1
≥1
10
0
64
940
35386
1523899
41712358
≥1
≥1
≥1
≥1
11
4
130
4836
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
12
3
257
8211
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
5
491
27233
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
6
943
59310
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
6
1775
160520
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
10
3337
389280
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
11
6217
982811
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
15
11514
2432435
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
18
21248
6098400
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
21
39010
14953595
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
all
all
all
all
all
all
all
all
all
all
?
?
?
?
?
?
?
?
?
?

See Also

Dominoes and Z tetrominoDominoes and L pentomino