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 X pentomino

Prime rectangles: ≥ 0.

Rectangle tilings' solutions count (including symmetric)

Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Purple number - prime rectangle (unknown if weakly or strongly prime).

Red number - 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 \ h
1-20
N>0
1-20
?
21
?
?
N>0
?

Smallest tori tilings

Smallest known torus (5x9):

Smallest square torus (9x9):

Tori tilings' solutions count (including translations)

w \ h
1
2
3
4
5
6
7
8
9
1
0
2
0
0
3
0
0
0
4
0
0
0
0
5
0
0
0
0
0
6
0
0
0
0
0
0
7
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
9
0
0
0
0
90
0
126
0
≥1000

Smallest Baiocchi figures

Smallest known Baiocchi figure (area 21):

See Also

I tetromino and W pentominoI tetromino and Y pentomino