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 L pentomino

Prime rectangles: 30.

Smallest rectangle tilings

Smallest rectangle (2x9):

Smallest square (5x5):

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 \ h12345678910N>0
10
2000
300000
40000000
5000000088P
6000002020P3030P102102P
7000004646P5252P138138P200200P
8000007272P346346P≥1000≥1000C≥1000≥1000C≥1000≥1000C
9066P1212P164164C820820C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
1000000404404P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
1100000876876P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
120000017321732C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1301212P4848P35523552C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1402020P0076327632C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
15000001714817148C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
16000003805838058C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1702020P120120P7849478494C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1806060C176176C161486161486C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1905656P00346774346774C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
20000128128P751518751518C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
2103030P240240P16005341600534C≥1≥1C??????????all
220140140C13601360C33811383381138C≥1≥1C??????????all
230224224C0071581967158196C≥1≥1C??????????all
240144144P11521152P1526889215268892C≥1≥1C??????????all
2504242P420420P3270441232704412C≥1≥1C??????????all
260280280C63366336C≥1≥1C≥1≥1C??????????all
270672672C25602560C≥1≥1C≥1≥1C??????????all
280720720C61446144P≥1≥1C≥1≥1C??????????all
290408408P42564256C≥1≥1C≥1≥1C??????????all
300504504C2336023360C≥1≥1C≥1≥1C??????????all
31016801680C3020830208C≥1≥1C≥1≥1C??????????all
32026402640C2572825728P≥1≥1C≥1≥1C??????????all
33021842184C4606446064C≥1≥1C≥1≥1C??????????all
34016721672C7600076000C≥1≥1C≥1≥1C??????????all
35036963696C206336206336C≥1≥1C≥1≥1C??????????all
36079207920C131328131328C≥1≥1C≥1≥1C??????????all
37092429242C324512324512C≥1≥1C≥1≥1C??????????all
38071447144C308896308896C≥1≥1C≥1≥1C??????????all
39093129312C10752001075200C≥1≥1C≥1≥1C??????????all
4002059220592C925440925440C≥1≥1C≥1≥1C??????????all
N>0xallallallallallallallallall

See Also

I tetromino and I pentominoI tetromino and N pentomino