POLYOMINO TILINGS

Polyomino Tilings

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O 9-omino

Area: 9.

Size: 3x3.

Is rectangular: yes.

Is convex: yes.

Holes: 0.

Order: 1.

Square order: 1.

Odd order: 1.

Prime rectangles: ≥ 1.

Smallest rectangle tilings

Smallest rectangle and smallest square and smallest odd rectangle (3x3):

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
1-2
0
3
0
1
4-5
0
0
0
6
0
1
0
1
7
0
0
0
0
0
8
0
0
0
0
0
0
9
0
≥1
0
≥1
?
?
≥1
10
0
0
0
0
0
0
?
0
11
0
0
0
0
0
0
?
0
0
12
0
≥1
0
≥1
0
0
≥1
0
0
≥1
13
0
0
0
0
0
0
?
0
0
0
0
14
0
0
0
0
0
0
?
0
0
0
0
0
15
0
≥1
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
16
0
0
0
0
0
0
?
0
0
0
0
0
0
0
17
0
0
0
0
0
0
?
0
0
0
0
0
0
0
0
18
0
≥1
0
≥1
?
?
≥1
?
?
≥1
?
?
≥1
?
?
≥1
19
0
0
0
0
0
0
?
0
0
0
0
0
0
0
0
?
0
20
0
0
0
0
0
0
?
0
0
0
0
0
0
0
0
?
0
0
21
0
≥1
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
?
N>0
x
3k
x
3k
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Smallest prime reptiles

Smallest prime reptile (9Ox2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
1²
2²
3²
4²
5²
O 9-omino
1
1
1
1
1

See Also

L1 9-ominoP1 9-omino