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.

I triomino and Z pentomino¶

Prime rectangles: ≥ 24.

Smallest rectangle tilings¶

Smallest rectangle (6x7):

Smallest square (7x7):

Rectangle tilings' solutions count (including symmetric)¶

Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Purple number - prime rectangle (unknown if weakly or strongly prime).

Red number - 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.

Smallest prime reptiles¶

Smallest prime reptiles (3Ix5, 5Zx2):

Reptile tilings' solutions count (including symmetric)¶

Smallest common multiples¶

Smallest known common multiple (area 30):

Common multiples' solutions count (excluding symmetric)¶

See Also¶