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 tetromino and Z tetromino

Prime rectangles: ≥ 9.

Smallest rectangle tilings

Smallest rectangle (5x8):

Smallest square (8x8):

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 \ h1-2345678910N>0
1-20
3000
400000
5000000
600000000
7000000000
80000066P3030P118118P540540P
900000000017701770P0
1000000000086468646C000
110000000003982639826C0004k
12000009090P15031503P1622016220P171293171293C≥1000≥1000P≥1000≥1000Call
13000000000594542594542C0004k
1400000000024165792416579C0???
150000000001022688010226880C0??4k
1600000964964C6282562825C16778281677828C≥23400000≥23400000C≥1000≥1000C≥1≥1Call
N>0x??4k?4kall4k?

See Also

I tetromino and T tetrominoI tetromino and I pentomino