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 tetromino, X pentomino and Z pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (8x13):

Smallest square (12x12):

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 \ h1234567891011121314151617
100
20000
3000000
400000000
50000000000
6000000000000
700000000000000
80000000000000000
9000000000000000000
1000000000000000000000
110000000000000000000000
12000000000000000000≥1≥1≥1≥1≥1≥1
1300000000000000≥1≥10000≥1≥1≥1≥1≥1≥1
1400000000000000≥1≥100≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1
1500000000000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1
1600000000000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1
17000000000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1
1800000000000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1
1900000000000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1
200000000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1

See Also

I tetromino, T tetromino and X pentominoN pentomino, T pentomino and X pentomino