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 V pentomino

Prime rectangles: ≥ 35.

Smallest rectangle tilings

Smallest known rectangle (8x16):

Smallest square (12x12):

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
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
8
40
13
0
0
0
0
0
0
0
0
0
0
0
140
0
14
0
0
0
0
0
0
0
0
0
10
0
300
0
≥100
15
0
0
0
0
0
0
0
0
0
0
0
1634
?
?
≥100
16
0
0
0
0
0
0
0
16
0
24
0
4656
?
?
?
≥256
17
0
0
0
0
0
0
0
0
0
0
0
≥12000
?
?
?
?
?
18
0
0
0
0
0
0
0
72
14
140
7522
≥100
≥100
?
?
≥1
≥1
≥1
19
0
0
0
0
0
0
0
0
0
0
?
≥100
?
?
?
?
?
≥1
?
20
0
0
0
0
0
0
0
40
0
476
?
≥100
?
≥1
?
≥1
?
≥1
?
≥1
21
0
0
0
0
0
0
0
0
40
0
?
≥100
?
?
?
?
?
≥1
?
?
22
0
0
0
0
0
0
0
82
0
2350
?
≥100
?
≥1
?
≥1
?
≥1
?
≥1
23
0
0
0
0
0
0
0
0
0
0
?
≥1
?
?
?
?
?
≥1
?
?
24
0
0
0
0
0
0
0
344
286
13128
≥100
≥1
≥100
≥1
≥1
≥1
≥1
≥1
≥1
≥1
25
0
0
0
0
0
0
0
0
0
0
?
≥1
?
?
?
?
?
≥1
?
?
26
0
0
0
0
0
0
0
1592
0
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
27
0
0
0
0
0
0
0
0
1624
?
?
≥1
?
?
≥1
?
?
≥1
?
?
28
0
0
0
0
0
0
0
916
0
≥100
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
29
0
0
0
0
0
0
0
0
0
?
?
≥1
?
?
?
?
?
≥1
?
?
30
0
0
0
0
0
0
0
2652
10602
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
31
?
?
?
?
?
?
?
0
?
?
?
≥1
?
?
?
?
?
≥1
?
?
32
?
?
?
?
?
?
?
7828
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
33
?
?
?
?
?
?
?
?
≥100
?
?
≥1
?
?
?
?
?
≥1
?
?
34
?
?
?
?
?
?
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
35
?
?
?
?
?
?
?
?
?
?
?
≥1
?
?
?
?
?
≥1
?
?
36
?
?
?
?
?
?
?
≥1
≥100
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1

See Also

Z tetromino and U pentominoZ tetromino and Y pentomino