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.

Tetrominoes¶

Prime rectangles: ≥ 11.

Smallest rectangle tilings¶

Smallest rectangles (3x8, 4x6):

Smallest square (6x6):

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 (4Ix3, 4Ox3, 4Lx3, 4Tx3, 4Zx3):

Reptile tilings' solutions count (including symmetric)¶

Smallest common multiples¶

Smallest common multiple (area 32):

Common multiples' solutions count (excluding symmetric)¶

Attributions¶

1. Smallest known common multiple found by Livio Zucca (http://www.iread.it/lz/4chall.html)

See Also¶