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 Z pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (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
80000000022000000
9000000000000000000
10000000008888112112276276≥1000≥1000≥1000≥1000
11000000000000000000≥1000≥100000
1200000000242400000000≥1000≥10000000
13000000000000000000≥1000≥1000000000
1400000000666600000000≥1000≥100000000000
150000000000304304≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
160000000017217200000000≥1000≥100000000000≥1000≥1000
17000000000000000000≥1000≥100000000000≥1000≥1000
180000000043243200000000≥1000≥100000000000≥1000≥1000
19000000000000000000≥1000≥100000000000≥1000≥1000
2000000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
21000000000000000000≥1000≥100000000000≥1000≥1000
2200000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
23000000000000000000≥1000≥100000000000≥1000≥1000
2400000000≥1000≥100000000000≥1000≥100000000000≥1000≥1000
250000000000≥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 Y pentominoL pentomino and A hexomino