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You may also see list of all polyomino sets for which data is available here.

Prime rectangles: ≥ 5.

Smallest rectangle (4x5):

Smallest square (8x8):

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

1-3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

N>0

1-3

0

4

0

0

5

0

0

6

0

0

0

7

0

0

0

0

8

0

9

0

0

0

0

?

10

0

0

0

0

?

?

11

0

0

0

0

?

?

?

12

0

13

0

0

0

0

?

?

?

?

14

0

0

0

0

?

?

?

?

?

15

0

0

0

0

?

?

?

?

?

?

16

0

17

0

?

?

?

?

?

?

?

?

?

?

18

0

?

?

?

?

?

?

?

?

?

?

?

19

0

?

?

?

?

?

?

?

?

?

?

?

?

20

0

21

0

?

?

?

?

?

?

?

?

?

?

?

?

?

N>0

x

all

?

?

?

all

?

?

?

all

?

?

?

all

?

?

?

?

Smallest common multiple (area 24):

Smallest known common multiple without holes (area 36):

Smallest known convex common multiple (area 48):

- Smallest rectangle and square found by Dmitry Grekov
- Solutions counted by Dmitry Grekov
- Smallest common multiple found by Jorge Mireles
- Holeless common multiple found by Dmitry Grekov
- Convex common multiple found by Dmitry Grekov