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.


Z tetromino and L pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (3x6):

Smallest square (6x6):

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
50000000000
6000022002288
70000006600141400
80000000088124124192192728728
9000000161600126126380380≥1000≥1000≥1000≥1000
10000000002424220220≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
110000008844≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
120000444848150150≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1300000088120120≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
14000000180180842842≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
150000002626≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

See Also

Z tetromino and I pentominoZ tetromino and P pentomino