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 tetromino and O tetromino

Prime rectangles: ≥ 6.

Smallest rectangle tilings

Smallest rectangles (2x6, 3x4):

Smallest square (4x4):

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 \ h123456789N>0
10
2000
3000
400022P66P
50001313P0
6022P03030C0254254C
70006060C000
8033P1010C135135C378378C≥1000≥1000C≥1000≥1000C≥1000≥1000C
9000271271C000≥1000≥1000C0
10077P0575575C0≥1000≥1000C0≥1000≥1000C02k
11000≥1000≥1000C000≥1000≥1000C04k
1201111C4040C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
13000≥1000≥1000C000≥1000≥1000C04k
1402020C0≥1000≥1000C0≥1000≥1000C0≥1000≥1000C02k
15000≥1000≥1000C000≥1000≥1000C04k
N>0x2k4kall4k2k4kall4k

See Also

I tetromino and L tetrominoI tetromino and T tetromino