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.


T tetromino and T pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (5x12):

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 \ h12345678910111213
100
20000
3000000
400000000
50000000000
6000000000000
700000000000000
80000000000000000
9000000000000008800
1000000000000000000000
11000000000000008810102200
1200000000220000424228428444302302≥1000≥1000
1300000000000000270270444400≥1000≥1000≥1000≥1000≥1000≥1000
140000000000000000161600232232≥1000≥1000≥1000≥1000
15000000000000002622622842841414330330≥1000≥1000≥1000≥1000
1600000000000000≥1000≥1000≥1000≥10008282≥1000≥1000≥1000≥1000≥1000≥1000
1700000000000088≥1000≥1000≥1000≥10007070≥1000≥1000≥1000≥1000≥1000≥1000
18000000000000002242243643642626≥1000≥1000≥1000≥1000≥1000≥1000
1900000000000000≥1000≥1000≥1000≥1000618618≥1000≥1000≥1000≥1000≥1000≥1000
2000000000000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

See Also

T tetromino and R pentominoT tetromino and U pentomino