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.


O tetromino and O hexomino

Prime rectangles: ≥ 7.

Smallest rectangle tilings

Smallest rectangle (2x5):

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 \ h123456789101112N>0
10
2000
30000
4000000
5022P044C0
6000022P88C1212P
7033P099C04545C0
8033P01515C2626C8989C280280C818818C
9044P02424C0226226C026702670C0
10066C04848C6666C546546C15111511C82548254C≥10000≥10000C≥10000≥10000C
11099P08181C012431243C0≥10000≥10000C0≥10000≥10000C0
1201010C0142142C162162C30363036C79377937C≥10000≥10000C≥10000≥10000C≥10000≥10000C≥10000≥10000C≥10000≥10000C
1301616C0256256C070567056C0≥10000≥10000C0≥10000≥10000C0≥10000≥10000C2k
1402020C0440440C418418C≥10000≥10000C≥10000≥10000C≥10000≥10000C≥10000≥10000C≥10000≥10000C≥10000≥10000C≥10000≥10000Call
1502727C0783783C0≥10000≥10000C0≥10000≥10000C0≥10000≥10000C0≥10000≥10000C2k
1603636C013681368C10541054C≥10000≥10000C≥10000≥10000C≥10000≥10000C≥10000≥10000C≥10000≥10000C≥10000≥10000C≥10000≥10000Call
N>0xallxall2kall2kall2kall2kall

See Also

O tetromino and L hexominoO tetromino and P hexomino