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.


T tetromino and Q hexomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (4x9):

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
1-3
4
5-7
8
9
10-11
12
13-15
16
17
18
19
20
N>0
1-3
?
4
?
?
5-7
?
?
?
8
?
?
?
?
9
?
≥1
?
≥1
?
10-11
?
?
?
?
?
?
12
?
?
?
?
≥1
?
?
13-15
?
?
?
?
?
?
?
?
16
?
?
?
?
≥1
?
?
?
?
17
?
?
?
?
?
?
?
?
?
?
18
?
≥1
?
≥1
?
?
≥1
?
≥1
?
?
19
?
?
?
?
?
?
?
?
?
?
?
?
20
?
?
?
?
≥1
?
?
?
?
?
≥1
?
?
21
?
?
?
?
?
?
?
?
?
?
?
?
?
?
N>0
?
?
?
?
?
?
?
?
?
?
?
?
?

See Also

T tetromino and P hexominoT tetromino and R1 hexomino