# 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.

## 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
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
N>0
x
3k
x
3k
?
?
?
?
?
?
?
?
?
?
?
?

## Smallest prime reptiles¶

Smallest prime reptile (9Ox2):

polyomino \ n²
O 9-omino
1
1
1
1
1