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 Z pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle and 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 \ h12345678910111213
100
20000
3000000
400000000
50000000000
6000000000022
700000000000000
80000000000440088
9000000000000000000
10000000000066002121006262
110000000000000000000000
12000000000014140055550022422400≥1000≥1000
1300000000000000000000000000
1400000000002626001221220072672600≥1000≥100000
1500000000000000000000000000
16000000000042420030530500≥1000≥100000≥1000≥100000
1700000000000000000000000000
18000000000080800072772700≥1000≥100000≥1000≥100000
1900000000000000000000000000
20000000000014614600≥1000≥100000≥1000≥100000≥1000≥100000

See Also

O tetromino and Y pentominoO tetromino and A hexomino