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.


I pentomino and Y pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (5x6):

Smallest square (10x10):

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 \ h12345678910
100
20000
3000000
400000000
50000000000
6000000004400
700000000880000
8000000001212000000
900000000161600000000
10000000006868446446≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
110000000019819800000000≥1000≥1000
120000000034234200000000≥1000≥1000
130000000051051000000000≥1000≥1000
140000000070270200000000≥1000≥1000
1500000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

See Also

I pentomino and W pentominoI pentomino and Z pentomino