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 T1 hexomino

Prime rectangles: 7.

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 \ h1-23456N>0
1-20
3000
4022P88P
5044P1818P5656P
6066P4646C174174C≥1≥1C
7088P102102C524524C≥1≥1Call
801414C234234C16341634C≥1≥1Call
N>0xallallallall

Smallest common multiples

Smallest common multiple (area 6):

Common multiples' solutions count (excluding symmetric)

area6
solutions1P

See Also

Monominoes and Z pentominoMonominoes and O1 heptomino