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.


C hexomino

Area: 6.

Size: 2x4.

Holes: 0.

Prime rectangles: 0.

Smallest rectangle tilings

No rectangles exist.

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 torus (3x4):

Smallest square torus (12x12):

Tori tilings' solutions count (including translations)

w \ h
1
2
3
4
5
6
7
8
9
10
11
12
1
0
2
0
0
3
0
0
0
4
0
0
12
0
5
0
0
0
0
0
6
0
0
0
48
0
0
7
0
0
0
0
0
0
0
8
0
0
12
0
0
48
0
0
9
0
0
0
192
0
0
0
192
0
10
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
12
0
0
12
768
0
48
0
768
192
0
0
1632
13
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
3072
0
0
0
3072
0
0
0
3072
16
0
0
12
0
0
48
0
0
192
0
0
768
17
0
0
0
0
0
0
0
0
0
0
0
0
18
0
0
0
≥10000
0
0
0
≥10000
0
0
0
≥10000
19
0
0
0
0
0
0
0
0
0
0
0
0
20
0
0
12
0
0
48
0
0
192
0
0
768
21
0
0
0
≥10000
0
0
0
≥10000
0
0
0
≥10000
22
0
0
0
0
0
0
0
0
0
0
0
0
23
0
0
0
0
0
0
0
0
0
0
0
0
24
0
0
12
≥10000
0
48
0
≥10000
192
0
0
≥10000

See Also

B hexominoD hexomino