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.


X pentomino and Y pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle and smallest known square (5x5):

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
1-4
5
6-9
10
11-14
15
16-19
20
N>0
1-4
?
5
?
≥1
6-9
?
?
?
10
?
≥1
?
≥1
11-14
?
?
?
?
?
15
?
≥1
?
≥1
?
≥1
16-19
?
?
?
?
?
?
?
20
?
≥1
?
≥1
?
≥1
?
≥1
21
?
?
?
?
?
?
?
?
?
N>0
?
?
?
?
?
?
?
?

See Also

W pentomino and Y2 hexominoX pentomino and A hexomino