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 pentomino and Y pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangles (4x10, 5x8):

Smallest square (10x10):

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 \ h123456789101112131415
100
20000
3000000
400000000
50000000000
6000000000000
700000000000000
8000000001212000000
900000000323200000000
1000000088110110576576≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
110000000012812800000000≥1000≥100000
120000000055255200000000≥1000≥10000000
130000000052052000000000≥1000≥1000000000
1400000000≥1000≥100000000000≥1000≥100000000000
15000000168168≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1600000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
1700000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
1800000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
1900000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
20000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
2100000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
2200000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
2300000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
2400000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
25000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

See Also

L pentomino and X pentominoL pentomino and Z pentomino