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 Z tetromino

Prime rectangles: ≥ 5.

Smallest rectangle tilings

Smallest rectangle (3x4):

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 \ h1-2345N>0
1-20
300
4066P3232P
500168168P0
606464P763763C81688168P?
70033143314C0?
80500500C1395113951C317174317174C?
900≥1≥1C0?
10034923492C≥1≥1C≥1≥1C?
1100≥1≥1C0?
N>0x2kall2k

Smallest prime reptiles

Smallest prime reptiles (2Ix3, 4Zx2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I domino0064P13951P≥1P
Z tetromino09P24964P≥194630401C≥1P

Smallest common multiples

Smallest common multiple (area 4):

Common multiples' solutions count (excluding symmetric)

area4
solutions1P

See Also

Dominoes and T tetrominoDominoes and I pentomino