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 9-omino

Area: 9.

Size: 1x9.

Is rectangular: yes.

Is convex: yes.

Holes: 0.

Order: 1.

Square order: 9.

Odd order: 1.

Prime rectangles: 1.

Smallest rectangle tilings

Smallest rectangle and smallest odd rectangle (1x9):

Smallest square (9x9):

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
N>0
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
1
1
1
1
1
1
1
1
2
10
0
0
0
0
0
0
0
0
3
0
11
0
0
0
0
0
0
0
0
4
0
0
12
0
0
0
0
0
0
0
0
5
0
0
0
13
0
0
0
0
0
0
0
0
6
0
0
0
0
14
0
0
0
0
0
0
0
0
7
0
0
0
0
0
15
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
17
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
18
1
1
1
1
1
1
1
1
12
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
0
0
0
0
0
0
≥1
0
0
0
0
0
0
0
0
≥1
?
20
0
0
0
0
0
0
0
0
≥1
0
0
0
0
0
0
0
0
≥1
?
N>0
9k
9k
9k
9k
9k
9k
9k
9k
all
9k
9k
9k
9k
9k
9k
9k
9k
all

Smallest prime reptiles

Smallest prime reptile (9Ix2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I 9-omino
1
1
1
1
1

See Also

B1 9-ominoL1 9-omino