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.


Monominoes and O1 heptomino

Prime rectangles: 6.

Smallest rectangle tilings

Smallest rectangle and smallest square (3x3):

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 \ h1-23456
1-20
3044P
4088P1616P
501212P2626P5858P
603232C100100C238238C18081808C
N>0xallallallall

Smallest prime reptiles

Smallest prime reptiles (1Ox3, 7O1x2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
O monomino004P16P
O1 heptomino07P505678P≥50000C

Smallest common multiples

Smallest common multiple (area 7):

Common multiples' solutions count (excluding symmetric)

area7
solutions1P

See Also

Monominoes and T1 hexominoDominoes and I triomino