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.


L tetromino and O tetromino

Prime rectangles: 6.

Smallest rectangle tilings

Smallest rectangles (2x6, 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 \ h12345678N>0
10
2000
3000
400066P88P
50004848P0
6044P09898C0≥1000≥1000C
7000378378C000
8066P4444C880880C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
9000≥1000≥1000C000≥1000≥1000C4k
1002020P0≥1000≥1000C0≥1000≥1000C0≥1000≥1000C2k
11000≥1000≥1000C000≥1≥1C4k
1203434C384384C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
13000≥1000≥1000C000≥1≥1C4k
1408484C0≥1000≥1000C0≥1≥1C0≥1≥1C2k
15000≥1000≥1000C000≥1≥1C4k
160154154C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
17000≥1000≥1000C000≥1≥1C4k
180340340C0≥1000≥1000C0≥1≥1C0≥1≥1C2k
19000≥1000≥1000C000≥1≥1C4k
200650650C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0x2k4kall4k2k4kall

See Also

I tetromino and U heptominoL tetromino and T tetromino