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.


Y pentomino and T2 hexomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (6x9):

Smallest known square (18x18):

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
1-5
6
7-8
9
10-11
12
13-14
15
16-17
18
19-20
N>0
1-5
?
6
?
?
7-8
?
?
?
9
?
≥1
?
?
10-11
?
?
?
?
?
12
?
?
?
≥1
?
?
13-14
?
?
?
?
?
?
?
15
?
?
?
?
?
?
?
?
16-17
?
?
?
?
?
?
?
?
?
18
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
19-20
?
?
?
?
?
?
?
?
?
?
?
21
?
?
?
?
?
?
?
?
?
≥1
?
?
N>0
?
?
?
?
?
?
?
?
?
?
?

See Also

Y pentomino and T1 hexominoY pentomino and T3 hexomino