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 L pentomino

Prime rectangles: 22.

Smallest rectangle tilings

Smallest rectangles (2x9, 3x6):

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
500000004040P
600044P44P9292P594594C
70001212P3030P372372P≥1000≥1000C≥1000≥1000C
8000004444P12441244P≥1000≥1000C≥1000≥1000C≥1000≥1000C
9088P88P318318C33203320C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
1000000520520P2275622756C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
110000028802880P6500865008C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
120002424C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1302424P160160C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1402424P336336C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
15000320320C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
16000344344C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1706464P128128P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1809696C256256C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1906464P16161616C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
2000061286128C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
210160160P1168011680C??????????????all
220320320C1510415104C??????????????all
230320320C1644816448C??????????????all
240160160P1208012080C??????????????all
250384384P2246422464C??????????????all
260960960C8214482144C??????????????all
27012801280C236864236864C??????????????all
280960960C448032448032C??????????????all
29012801280P645632645632C??????????????all
30026882688C748416748416C??????????????all
N>0xallallallallallallallallall

See Also

L tetromino and I pentominoL tetromino and N pentomino