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 L tetromino

Prime rectangles: ≥ 16.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (4x4):

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 \ h12345N>0
10
2000
300000
40000088P
500088P7878P576576P
60003232P228228P32203220Call
7088P104104P10201020C1791617916Call
8000248248P36803680C105712105712Call
9000568568P1403214032C652764652764Call
1002424P12101210C5203052030C39346143934614Call
1102424P28122812C200860200860C2355563223555632Call
1200070307030C748570748570C≥1≥1Call
1306464P1848818488C28417682841768C≥1≥1Call
1409696C4777847778C1065749010657490C≥1≥1Call
1506464P119504119504C4014313040143130C≥1≥1Call
160160160P≥1≥1C≥1≥1C≥1≥1Call
170320320C≥1≥1C≥1≥1C≥1≥1Call
180320320C≥1≥1C≥1≥1C≥1≥1Call
190544544P≥1≥1C≥1≥1C≥1≥1Call
200960960C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallall

See Also

L triomino and I tetrominoL triomino and O tetromino