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.


Dominoes and L pentomino

Prime rectangles: ≥ 13.

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 \ h123456N>0
10
2000
300000
400022P2020P
50001616P170170P11441144P
6044P3838P914914C94009400C116392116392C
701212P128128P41784178C5483654836C11073901107390C?
802626P332332C1861118611C399640399640C1207567612075676C?
905656P976976C7984479844C24451242445124C118454298118454298C?
100112112P25562556C346138346138C1681473216814732C≥1≥1C?
110≥1≥1P≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
120≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
N>0xallallallallall

See Also

Dominoes and I pentominoDominoes and N pentomino