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.


O tetromino and V pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle and smallest square (3x3):

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 \ h12345678
100
20000
3000044
400000000
50000000000
600001616003232256256
70000000000484800
800000000007687680020482048
9000064640000416041600000
10000000000015361536001203212032
11000000000016464164640000
120000256256001024102468096680961100811008661248661248
13000000000041056410560000
14000000000033152033152000≥1≥1
1500001024102400001130608113060800??

See Also

O tetromino and T pentominoO tetromino and Y pentomino