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.

Prime rectangles: ≥ 11.

Smallest rectangles (3x8, 4x6):

Smallest square (6x6):

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

1-2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

N>0

1-2

0

3

0

0

4

0

0

0

5

0

0

0

0

6

0

0

0

7

0

0

0

0

0

8

0

9

0

0

0

0

0

0

10

0

0

0

0

0

11

0

0

0

0

0

0

0

0

12

0

13

0

0

0

0

0

0

0

0

0

14

0

0

0

0

0

0

0

15

0

0

0

0

0

0

0

0

0

0

0

16

0

17

0

0

0

0

0

0

0

0

0

0

0

0

18

0

0

0

0

0

0

0

0

0

19

0

0

0

0

0

0

0

0

0

0

0

0

0

0

20

0

21

0

0

0

0

0

0

0

0

0

0

0

0

0

0

?

N>0

x

4k

all

4k

2k

4k

all

4k

2k

4k

all

4k

2k

4k

all

4k

2k

4k

all

Smallest prime reptiles (4Ix3, 4Ox3, 4Lx3, 4Tx3, 4Zx3):

polyomino \ n²

1²

2²

3²

I tetromino

0

0

L tetromino

0

0

O tetromino

0

0

T tetromino

0

0

Z tetromino

0

0

Smallest common multiple (area 32):

- Smallest known common multiple found by Livio Zucca (http://www.iread.it/lz/4chall.html)