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 pentomino and R2 hexomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (13x42):

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
1-12
13
14-20
N>0
1-12
?
13
?
?
14-20
?
?
?
21
?
?
?
?
22
?
?
?
?
23
?
?
?
?
24
?
?
?
?
25
?
?
?
?
26
?
?
?
?
27
?
?
?
?
28
?
?
?
?
29
?
?
?
?
30
?
?
?
?
31
?
?
?
?
32
?
?
?
?
33
?
?
?
?
34
?
?
?
?
35
?
?
?
?
36
?
?
?
?
37
?
?
?
?
38
?
?
?
?
39
?
?
?
?
40
?
?
?
?
41
?
?
?
?
42
?
≥1
?
?
N>0
?
?
?

See Also

I pentomino and R1 hexominoI pentomino and S hexomino