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 T1 hexomino

Prime rectangles: ≥ 12.

Smallest rectangle tilings

Smallest rectangle (4x5):

Smallest square (6x6):

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 \ h1-23456N>0
1-20
300
400000
50022P0
600044P204204P984984P
7002424P01077010770P?
8011P7070P68306830C6098760987C?
900266266P0≥1≥1C?
10077P840840C≥1≥1C≥1≥1C?
1100≥1≥1C0≥1≥1C?
1203838P≥1≥1C≥1≥1C≥1≥1C?
1300≥1≥1C0≥1≥1C?
140186186P≥1≥1C≥1≥1C≥1≥1C?
1500≥1≥1C0≥1≥1C?
160860860C≥1≥1C≥1≥1C≥1≥1C?
N>0x2kall2kall

Smallest common multiples

Smallest common multiple (area 12):

Common multiples' solutions count (excluding symmetric)

area612
solutions05P

See Also

Dominoes and Z pentominoI triomino and I tetromino