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 pentomino and Y2 hexomino

Prime rectangles: ≥ 1.

Smallest rectangle tilings

Smallest known rectangle and smallest known square (36x36):

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
1-22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
N>0
1-22
0
23
0
0
24
0
0
0
25
0
0
0
0
26
0
0
0
0
0
27
0
0
0
0
0
0
28
0
0
0
0
0
0
?
29
0
0
0
0
0
0
?
?
30
0
0
0
0
0
0
?
?
?
31
0
0
0
0
0
0
?
?
?
?
32
0
0
0
0
0
0
?
?
?
?
?
33
0
0
0
0
0
0
?
?
?
?
?
?
34
0
0
0
0
0
?
?
?
?
?
?
?
?
35
0
0
0
0
0
?
?
?
?
?
?
?
?
?
36
0
0
0
0
0
?
?
?
?
?
?
?
?
?
≥1
37
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
38
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
39
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
40
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
41
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
42
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
43
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
44
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
45
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
46
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
47
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
48
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
49
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
50
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
51
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
52
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
53
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
54
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
55
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
56
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
N>0
x
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Attributions

  1. Smallest rectangle taken from here http://www2.stetson.edu/~efriedma/mathmagic/0810.html

See Also

Z pentomino and Y1 hexominoC hexomino and I hexomino