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.


L tetromino and I pentomino

Prime rectangles: 28.

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 \ h12345678910N>0
10
2000
300000
40000000
5000000000
600022P0088P7272C
70000066P7676P11781178P84888488P
80000000184184P12601260C1657216572C108644108644P
9066P006868C33443344P77967796C161940161940C12276861227686C≥1000≥1000C
10000000096569656P5770257702C594636594636C88870628887062C≥1000≥1000C≥1000≥1000C
110004646P530530P1821218212P374586374586C25507182550718C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1200044C6868P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1302020P2828P40924092C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1401212P188188P744744C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
15000002670226702P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
16000332332P78267826C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1705656P612612C164592164592C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1806060C120120C6846268462C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1902020P21402140C954746954746C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
2000014921492C517478517478C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
210144144P17721772P53358745335874C????????????all
220224224C1002810028C36773723677372C????????????all
230140140C36803680C2898923828989238C????????????all
2403030P1474814748C2463607624636076C????????????all
250352352P4038040380C154491878154491878C????????????all
260720720C1363413634C??????????????all
270672672C9735697356C??????????????all
280280280C146864146864C??????????????all
290874874P9345293452C??????????????all
30021122112C534616534616C??????????????all
31026402640C493166493166C??????????????all
32016801680C717564717564C??????????????all
33024242424C25286562528656C??????????????all
34058805880C17274121727412C??????????????all
35091529152C48621924862192C??????????????all
36079207920C1058462010584620C??????????????all
37080488048C75931887593188C??????????????all
3801620016200C2825010028250100C??????????????all
3902919229192C4095013240950132C??????????????all
4003203232032C4270585242705852C??????????????all
N>0xallallallallallallallallall

See Also

L tetromino and Z tetrominoL tetromino and L pentomino