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.


L tetromino and T tetromino

Prime rectangles: 4.

Smallest rectangle tilings

Smallest rectangle (3x4):

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 \ h1-2345678910N>0
1-20
300
4044P00
5001616P0
6003434C0776776P
700128128P000
802424C198198C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
900832832C000≥1000≥1000C0
1000≥1000≥1000C0≥1000≥1000C0≥1000≥1000C0≥1000≥1000C
1100≥1000≥1000C000≥1000≥1000C004k
120160160C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1300≥1000≥1000C000≥1000≥1000C004k
1400≥1000≥1000C0≥1000≥1000C0≥1000≥1000C0≥1000≥1000C2k
1500≥1000≥1000C000≥1000≥1000C004k
160≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
N>0x4kall4k2k4kall4k2k

See Also

L tetromino and O tetrominoL tetromino and Z tetromino