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.


I pentomino and T pentomino

Prime rectangles: ≥ 6.

Smallest rectangle tilings

Smallest rectangle (10x11):

Smallest square (15x15):

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 \ h1-789101112131415N>0
1-70
800
9000
100000000
110004400
12000880000
130001212000000
14000161600000000
15044P88P3232684684≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1600017217200000000≥1000≥1000?
1700039239200000000≥1000≥1000?
1800071271200000000≥1000≥1000?
19000≥1000≥100000000000≥1000≥1000?
200112112P248248P≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
21000≥1000≥100000000000≥1000≥1000?
22000≥1000≥100000000000≥1000≥1000?
23000≥1000≥100000000000≥1000≥1000?
24000≥1000≥100000000000≥1000≥1000?
25018981898P47064706P≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
26000?????????????
27000?????????????
28000?????????????
29000?????????????
3002569625696C7173871738C?????????????
N>0x5k5kall?????

See Also

I pentomino and R pentominoI pentomino and U pentomino