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 N pentomino

Prime rectangles: ≥ 16.

Smallest rectangle tilings

Smallest rectangle (2x7):

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
40000044P
50001212P3838P624624P
600044P230230P26962696C2921229212C
7022P9292P12661266C2174421744C288536288536C?
8066P8484P56675667C111022111022C26745922674592C?
901616P580580P2433424334C743696743696C2480311024803110C?
100≥1≥1P≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
110≥1≥1P≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
120≥1≥1P≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
130≥1≥1P≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
140≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
N>0xallallallallall

See Also

Dominoes and L pentominoDominoes and P pentomino