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.


P1 9-omino

Area: 9.

Size: 2x6.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 2.

Square order: 4.

Odd order: 15.

Prime rectangles: ≥ 4.

Some facts:

Smallest rectangle tilings

Smallest rectangles (2x9, 3x6):

Smallest square (6x6):

Smallest odd rectangles (5x27, 9x15):

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
0
0
0
5
0
0
0
0
0
6
0
0
2
0
0
8
7
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
9
0
2
0
4
0
40
0
160
0
10
0
0
0
0
0
0
0
0
512
0
11
0
0
0
0
0
0
0
0
0
0
0
12
0
0
4
0
0
146
0
0
3288
0
0
≥100
13
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
14368
0
0
0
0
0
15
0
0
0
0
0
624
0
0
1536
0
0
≥100
0
0
≥100
16
0
0
0
0
0
0
0
0
54816
0
0
0
0
0
0
0
17
0
0
0
0
0
0
0
0
6144
0
0
0
0
0
0
0
0
18
0
4
8
18
72
2586
1256
38554
296200
≥100
≥100
≥100
≥100
≥100
≥100
≥100
≥100
≥100
19
0
0
0
0
0
0
0
0
20352
0
0
0
0
0
0
0
0
≥100
0
20
0
0
0
0
0
0
0
0
≥100
0
0
0
0
0
0
0
0
≥100
0
0
21
0
0
0
0
0
10608
0
0
≥100
0
0
≥100
0
0
≥100
0
0
≥100
0
0
3k
22
0
0
0
0
0
0
0
0
≥100
0
0
0
0
0
0
0
0
≥100
0
0
9k
23
0
0
0
0
0
0
0
0
≥100
0
0
0
0
0
0
0
0
≥100
0
0
9k
24
0
0
16
0
0
44034
0
0
≥100
0
0
≥100
0
0
≥100
0
0
≥100
0
0
3k
25
0
0
0
0
0
0
0
0
≥100
0
0
0
0
0
0
0
0
≥100
0
0
9k
26
0
0
0
0
0
0
0
0
≥100
0
0
0
0
0
0
0
0
≥100
0
0
9k
27
0
8
0
88
384
182120
61344
10036104
≥100
≥100
≥100
≥100
≥100
≥100
≥100
≥100
≥100
≥100
≥1
≥1
all
N>0
x
9k
6k
9k
9k
3k
9k
9k
all
9k
9k
3k
9k
9k
3k
9k
9k
all
9k
9k

Smallest prime reptiles

Smallest prime reptile (9P1x2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
1²
2²
3²
4²
5²
6²
7²
8²
9²
10²
11²
12²
P1 9-omino
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1

See Also

O 9-ominoP2 9-omino