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 triomino and P pentomino

Prime rectangles: ≥ 9.

Smallest rectangle tilings

Smallest rectangle (2x4):

Smallest square (4x4):

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
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1
0
2
0
0
3
0
0
0
4
0
4
0
32
5
0
0
0
40
128
6
0
0
0
240
740
≥1000
7
0
16
0
710
≥1000
≥1000
≥1000
8
0
24
0
≥1000
≥1000
≥1000
≥1000
≥1000
9
0
16
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
10
0
48
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
11
0
120
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
12
0
160
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
13
0
248
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
14
0
496
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
15
0
896
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
16
0
≥1000
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
≥1000
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
≥1000
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
≥1000
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
≥1000
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
≥1000
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
0
≥1000
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
23
0
≥1000
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
24
0
≥1000
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
25
0
≥1000
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
x
all
x
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all

See Also

L triomino and N pentominoL triomino and R pentomino