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.


Dominoes and O tetromino

Prime rectangles: ≥ 3.

Smallest rectangle tilings

Smallest rectangle (2x3):

Smallest square (4x4):

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 \ h1234N>0
10
2000
3022P0
4055P1818C128128C
501313P0498498C?
602929C132132C24912491C?
N>0xall2kall

Smallest prime reptiles

Smallest prime reptiles (2Ix2, 4Ox2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I domino??P?P
O tetromino??P?P

Smallest common multiples

Smallest common multiple (area 4):

Common multiples' solutions count (excluding symmetric)

area4
solutions1P

See Also

Dominoes and L tetrominoDominoes and T tetromino