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.


I triomino and L pentomino

Prime rectangles: ≥ 18.

Smallest rectangle tilings

Smallest rectangle (2x4):

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 \ h12345678N>0
10
2000
300000
4044P003232C
5000002828P100100P
600000200200C612612P24842484P
7088P00374374C24682468P1500415004C126404126404C
802020C0017121712C80948094C127048127048C10070281007028C1421604814216048C
901616P3232P33883388C2981029810C605412605412C81519248151924C≥1≥1Call
1001212P6464P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1105454C9696P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
120112112C360360P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
130124124C688688P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
140152152C10801080P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
150352352C25362536P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
160684684C45844584P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
170874874C73207320P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
180≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
190≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
200≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallallallallall

See Also

I triomino and I pentominoI triomino and N pentomino