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 triomino and I tetromino

Prime rectangles: ≥ 16.

Smallest rectangle tilings

Smallest rectangle (1x7):

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 \ h1234567N>0
100
20000
3000000
40000001212P
5000022P2323P1616P
6000033P4040P101101C348348C
722P44C1212C172172C778778C32563256C2388023880C
800002323P452452C18201820C1224112241C143972143972C?
900003939P981981C43754375C3840438404C729116729116C?
1033P99C8484C26942694C2356623566C217113217113C42312794231279C?
1133P99C177177C72817281C8439284392C11153241115324C2680624926806249C?
120022P318318C?????????
1344P1616C575575C?????????
1466C3636C11761176C?????????
1544P2424C22412241C?????????
1655P3535C40404040C?????????
171010C100100C77107710C?????????
181010C120120C1491614916C?????????
191111P121121C2768127681C?????????
201515C255255C5134251342C?????????
N>0allallallallallallall

See Also

Dominoes and T1 hexominoI triomino and L tetromino