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 P pentomino

Prime rectangles: 26.

Smallest rectangle tilings

Smallest rectangles (2x9, 3x6):

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 \ h12345678N>0
10
2000
300000
40000000
5000000000
600022P1212P2424P124124C
7000004646P2828P486486C23122312P
800022P8484P324324P≥1000≥1000C≥1000≥1000C≥1000≥1000C
9066P00186186C416416P≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1000066P308308P29622962P≥1000≥1000C≥1000≥1000C≥1000≥1000Call
110002020P750750P50485048P≥1000≥1000C≥1000≥1000C≥1000≥1000Call
120001414C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1301212P00≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1402020P106106C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
15000120120P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
160005656C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1702020P296296C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1806060C686686C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1905656P532532C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
20000930930C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
2103030P≥1≥1C??????????all
220140140C≥1≥1C??????????all
230224224C≥1≥1C??????????all
240144144P≥1≥1C??????????all
2504242P≥1≥1C??????????all
260280280C≥1≥1C??????????all
270672672C≥1≥1C??????????all
280720720C≥1≥1C??????????all
290408408P≥1≥1C??????????all
300504504C≥1≥1C??????????all
N>0xallallallallallallall

See Also

I tetromino and N pentominoI tetromino and R pentomino