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 T tetromino

Prime rectangles: ≥ 6.

Smallest rectangle tilings

Smallest rectangle (4x5):

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 \ h1-3456789N>0
1-30
4000
5044P0
6066P000
7088P000
803434P122122C230230C524524C≥1000≥1000C
908080P000≥1000≥1000C0
100128128C01212P0≥1000≥1000C02k
110184184C000≥1000≥1000C04k
120578578C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
130≥1000≥1000C000≥1000≥1000C04k
140≥1000≥1000C0≥1000≥1000C0≥1000≥1000C02k
150≥1000≥1000C000≥1000≥1000C04k
N>0xall4k2k4kall4k

See Also

I tetromino and O tetrominoI tetromino and Z tetromino