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 pentomino and V pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (5x6):

Smallest square (10x10):

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 \ h123456789101112131415
100
20000
3000000
400000000
50000000000
6000000002200
700000000440000
80000000066000000
9000000008800000000
100000000010107070146146272272470470≥1000≥1000
1100000000181800000000≥1000≥100000
1200000000343400000000≥1000≥10000000
1300000000585800000000≥1000≥1000000000
1400000000909000000000≥1000≥100000000000
1500000000130130≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
160000000019019000000000≥1000≥100000000000≥1000≥1000
170000000029429400000000≥1000≥100000000000≥1000≥1000
180000000046846800000000≥1000≥100000000000≥1000≥1000
190000000073873800000000≥1000≥100000000000≥1000≥1000
2000000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
2100000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
2200000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
2300000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
2400000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
2500000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

See Also

I pentomino and U pentominoI pentomino and W pentomino