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.


Z tetromino and D hexomino

Prime rectangles: ≥ 26.

Smallest rectangle tilings

Smallest rectangle (4x8):

Smallest square (8x8):

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
0
0
0
6
0
0
0
0
0
0
7
0
0
0
0
0
0
0
8
0
0
0
4
4
0
16
48
9
0
0
0
0
0
4
0
156
0
10
0
0
0
9
0
0
0
≥1000
≥1000
≥1000
11
0
0
0
2
0
0
0
≥1000
0
≥1000
0
12
0
0
0
24
8
0
40
≥1000
≥1000
≥1000
≥1000
≥1000
13
0
0
0
16
0
16
0
≥1000
0
≥1000
0
≥1000
0
14
0
0
0
89
0
16
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
15
0
0
0
68
0
0
0
≥1000
0
≥1000
0
≥1000
0
≥1000
0
16
0
0
0
294
72
0
608
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
17
0
0
0
248
0
48
0
≥1000
0
≥1000
0
≥1000
0
≥1000
0
≥1
?
18
0
0
0
951
0
96
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
19
0
0
0
934
0
64
0
≥1000
0
≥1000
0
≥1000
0
≥1000
0
≥1
?
≥1
?
20
0
0
0
≥1000
298
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
21
0
0
0
≥1000
0
128
0
≥1000
0
≥1000
0
≥1000
0
≥1000
0
≥1
?
≥1
?
≥1
22
0
0
0
≥1000
0
384
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
23
0
0
0
≥1000
0
512
0
≥1000
0
≥1000
0
≥1000
0
≥1000
0
≥1
?
≥1
?
≥1
24
0
0
0
≥1000
≥1000
256
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
25
0
0
0
≥1000
0
320
0
≥1000
0
≥1000
0
≥1000
0
≥1000
0
≥1
?
≥1
?
≥1
26
0
0
0
≥1000
0
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
27
0
0
0
≥1000
0
≥1000
0
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
28
0
0
0
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
29
0
0
0
≥1000
0
≥1000
0
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
30
0
0
0
≥1000
0
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
31
0
0
0
≥1000
0
≥1000
0
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
32
0
0
0
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
33
0
0
0
≥1000
0
≥1000
0
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
34
0
0
0
≥1000
0
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
35
0
0
0
≥1000
0
≥1000
0
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1

See Also

Z tetromino and C hexominoZ tetromino and F hexomino