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 V 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
80000000000000000
9000000000022000000
1000000000008822661616318318
11000000000014144418181212648648648648
1200000000004466882626≥1000≥1000≥1000≥1000≥1000≥1000
13000000000026268834342020≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
14000000000064641010150150188188≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
150000000000646488474474228228≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
16000000000074742222340340972972≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1700000000002962963232≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1800000000004644647474≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
190000000000492492104104≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
200000000000964964190190≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

See Also

T tetromino and U pentominoT tetromino and W pentomino