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.


Z tetromino and P pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle (2x7):

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 \ h123456789
100
20000
3000000
400000000
50000000000
6000000440022
700220016160019419400
80000004400426426≥1000≥1000≥1≥1
9002200181800≥1000≥100000≥1≥100
100000004400≥1000≥1000≥1000≥1000≥1≥1≥1≥1
1100220017417400≥1000≥100000≥1≥1≥1≥1
1200880051651600≥1000≥1000≥1000≥1000≥1≥1≥1≥1
1300220077077000≥1000≥100000≥1≥1??
1400121200≥1000≥100000≥1000≥1000≥1000≥1000≥1≥1??
15002200≥1000≥100000≥1000≥1000??≥1≥1??

See Also

Z tetromino and L pentominoZ tetromino and T pentomino