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 triomino and Z tetromino

Prime rectangles: ≥ 8.

Smallest rectangle tilings

Smallest rectangle (2x5):

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 \ h1234567N>0
10
2000
30000
4000000
5022P02020C00
6000000176176C112112P
7022P05454C0055045504C1075210752P
8088P0390390C28882888C≥1≥1C≥1≥1Call
9022P0384384C00≥1≥1C≥1≥1Call
1001212C021162116C3245632456C≥1≥1C≥1≥1Call
1102626P060586058C1190411904P≥1≥1C≥1≥1Call
1201616C01364413644C354200354200C≥1≥1C≥1≥1Call
1305050C05080650806C231552231552C≥1≥1C≥1≥1Call
1408484C0123314123314C40785524078552C≥1≥1C≥1≥1Call
1508282C0361960361960C36309123630912C≥1≥1C≥1≥1Call
N>0xallxallallallall

See Also

L triomino and T tetrominoL triomino and I pentomino