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.


R pentomino and C hexomino

Prime rectangles: ≥ 32.

Smallest rectangle tilings

Smallest rectangle (5x8):

Smallest square (14x14):

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
1-4
5
6-7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-4
0
5
0
0
6-7
0
0
0
8
0
2
0
0
9
0
0
0
0
0
10
0
0
0
4
0
0
11
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
2
15
0
0
0
8
0
0
0
0
0
0
0
16
0
4
0
0
0
16
0
0
0
0
64
0
17
0
0
0
0
0
0
0
0
16
40
0
0
?
18
0
0
0
0
0
0
0
0
0
0
8
0
?
?
19
0
0
0
0
0
0
0
0
0
0
0
0
?
?
?
20
0
0
0
16
0
0
0
0
32
16
8
≥1
?
?
?
?
21
0
0
0
0
0
0
0
0
0
0
0
?
?
?
?
≥1
?
22
0
0
0
0
0
0
0
0
0
0
0
?
?
?
?
≥1
?
23
0
0
0
0
0
0
0
0
0
136
0
?
?
?
?
≥1
?
24
0
8
0
0
0
64
0
0
0
0
544
?
?
?
?
≥1
?
25
0
0
0
32
0
0
0
34
448
112
?
≥1
?
?
?
≥1
?
26
0
0
0
0
0
0
0
8
64
144
≥1
?
≥1
?
?
≥1
?
27
0
0
0
0
0
0
0
0
0
≥52
?
?
≥1
?
?
≥1
?
28
0
0
0
0
0
0
0
512
512
≥1
≥1
?
≥1
?
?
≥1
?
29
0
0
0
0
0
0
0
16
96
?
?
?
?
?
?
≥1
?
30
0
0
0
64
0
0
0
2
352
?
?
≥1
?
≥1
?
≥1
?
31
0
0
0
0
0
0
0
0
384
≥1
?
?
?
?
?
≥1
?
32
0
16
0
0
0
256
0
4
≥240
?
≥1
?
≥1
≥1
?
≥1
?
33
0
0
0
0
0
0
0
0
?
?
?
?
?
?
?
≥1
?
34
0
0
0
0
0
0
0
108
≥1
≥1
≥1
?
?
?
?
≥1
?
35
0
0
0
128
0
0
0
264
?
?
?
≥1
?
?
?
≥1
?
36
0
0
0
0
0
0
0
160
?
?
≥1
?
?
?
?
≥1
?
37
0
0
0
0
0
0
0
304
≥1
≥1
?
?
?
?
?
≥1
?
38
0
0
0
0
0
0
0
310
?
?
≥1
?
?
?
?
≥1
?
39
0
0
0
0
0
0
0
144
?
≥1
?
?
≥1
?
?
≥1
?
40
0
32
0
256
0
1024
0
560
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
?
x
?
x
?
x
?
?
?
?
?
?
?
?
?

See Also

R pentomino and B hexominoR pentomino and D hexomino