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.


Dominoes and I pentomino

Prime rectangles: ≥ 16.

Smallest rectangle tilings

Smallest rectangle (1x7):

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 \ h123456N>0
100
20000
3000000
400000000
500001616P2424P572572P
60022P66P7878C14511451C95769576C
722P77C138138C617617C1500015000C106161106161C?
8001414P7676P20342034C5064050640C681596681596C?
933P3232C847847C96049604C360302360302C58755805875580C?
10006464P940940P3538635386C15238991523899C4171235841712358C?
1144P130130C48364836C≥1≥1C≥1≥1C≥1≥1C?
1233P257257C82118211C≥1≥1C≥1≥1C≥1≥1C?
1355P491491C2723327233C≥1≥1C≥1≥1C≥1≥1C?
1466C943943C5931059310C≥1≥1C≥1≥1C≥1≥1C?
1566P17751775C160520160520C≥1≥1C≥1≥1C≥1≥1C?
161010C33373337C389280389280C≥1≥1C≥1≥1C≥1≥1C?
171111P62176217C982811982811C≥1≥1C≥1≥1C≥1≥1C?
181515C1151411514C24324352432435C≥1≥1C≥1≥1C≥1≥1C?
191818C2124821248C60984006098400C≥1≥1C≥1≥1C≥1≥1C?
202121C3901039010C1495359514953595C≥1≥1C≥1≥1C≥1≥1C?
N>0allallallallallall

See Also

Dominoes and Z tetrominoDominoes and L pentomino