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.


N pentomino and O1 15-omino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (16x30):

Rectangle tilings' solutions count (including symmetric)

Blue number (P) - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number (W) - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Red number (C) - 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 \ h1-131415161718192021N>0
1-130
14000
1500000
160000000
17000000000
1800000000000
190000000000000
2000000000000????
2100000000000????00
2200000000000????00?
2300000000000????00?
2400000000000????00?
2500000000000???????
2600000000000???????
2700000000000???????
2800000000000???????
2900000000000???????
3000000≥4≥4???????????
3100000?????????????
3200000?????????????
33000???????????????
34000???????????????
N>0x????????

See Also

N pentomino and O1 12-ominoN pentomino and P pentomino