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.


O tetromino and P pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (6x6):

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
60000001111008484
700440036360034434400
8000000464600745745≥1000≥1000≥1000≥1000
9006600989800≥1000≥100000≥1000≥100000
1000000011311300≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1100880042042000≥1000≥100000≥1000≥1000≥1000≥1000≥1000≥1000
1200121200≥1000≥100000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1300101000≥1000≥100000≥1000≥100000≥1000≥1000≥1000≥1000≥1000≥1000
1400242400≥1000≥100000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1500121200≥1000≥100000≥1000≥100000≥1000≥1000≥1000≥1000≥1000≥1000
1600404000≥1000≥100000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1700464600≥1000≥100000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1800606000≥1000≥100000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1900969600≥1000≥100000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
2000848400≥1000≥100000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

See Also

O tetromino and N pentominoO tetromino and T pentomino