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 Z pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle (3x7):

Smallest square (5x5):

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 \ h12345678910
100
20000
3000000
400000000
5000000002424
6000000004422
70000220044224224≥1000≥1000
800000000008080704704≥1000≥1000
900000022510510≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1000000044≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
110000001414≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
120000003636≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
13000022128128≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1400001414288288≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1500003232894894≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
16000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
17000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
18000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
19000022≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
2000002424≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

See Also

L tetromino and Y pentominoO tetromino and T tetromino