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 L pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle (3x5):

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 \ h12345678910
100
20000
3000000
400000000
5000044664040
600000000949400
7000000002802800000
800000000650650000000
900000000≥1000≥100000000000
1000662828156156≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1100000000≥1000≥100000000000≥1000≥1000
1200000000≥1000≥100000000000≥1000≥1000
1300000000≥1000≥100000000000≥1000≥1000
1400000000≥1000≥100000000000≥1000≥1000
15003232168168≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

See Also

Z tetromino and Y2 hexominoI pentomino and N pentomino