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 Z pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (10x12):

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
9000000000000000000
1000000000000000000000
110000000000000000000000
12000000000000000000441041046060
1300000000000000000022885845844040
1400000000000000002212121616≥1000≥1000≥1000≥1000
15000000000000000000883636≥1000≥1000≥1000≥1000
16000000000000008800600600≥1000≥1000≥1000≥1000≥1000≥1000
17000000000000008800324324386386≥1000≥1000≥1000≥1000
1800000000000000303000972972≥1000≥1000≥1000≥1000≥1000≥1000
190000000000000048481616≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
200000000000000040840888≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
21000000000000004624623030????????
2200000000000000≥1000≥10005858????????
2300000000000000≥1000≥1000140140????????
2400000000000000≥1000≥1000212212????????
2500000000000000≥1000≥1000≥1000≥1000????????
2600000000000000≥1000≥1000940940????????
2700000000000000≥1000≥1000≥1000≥1000????????
2800000000000000≥1000≥1000≥1000≥1000????????
2900000000000000≥1000≥1000≥1000≥1000????????
3000000000000000≥1000≥1000≥1000≥1000????????

See Also

T tetromino and Y pentominoT tetromino and A hexomino