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.


P3 octomino

Area: 8.

Size: 3x4.

Holes: 0.

Order: 2.

Square order: 2.

Prime rectangles: ≥ 4.

Smallest rectangle tilings

Smallest rectangle and smallest square (4x4):

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
1-3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-3
0
4
0
4
5
0
0
0
6
0
0
0
0
7
0
0
0
0
0
8
0
16
0
4
0
270
9
0
0
0
0
0
0
0
10
0
0
0
0
0
160
0
0
11
0
0
0
0
0
0
0
0
0
12
0
64
0
0
0
4688
0
0
0
≥100
13
0
0
0
0
0
0
0
0
0
0
?
14
0
0
0
0
0
4728
0
0
0
0
?
?
15
0
0
0
0
0
0
0
0
0
0
?
?
?
16
0
256
8
16
128
83716
≥100
≥100
≥100
≥100
≥1
≥1
≥1
≥1
17
0
0
0
0
0
0
0
0
0
0
?
?
?
≥1
?
18
0
0
0
0
0
122688
0
0
0
?
?
?
?
≥1
?
?
19
0
0
0
0
0
0
0
0
0
?
?
?
?
≥1
?
?
?
20
0
1024
0
0
0
1534376
0
0
0
≥1
?
?
?
≥1
?
?
?
≥1
21
0
0
0
0
0
0
0
0
0
?
?
?
?
≥1
?
?
?
?
?
22
0
0
0
0
0
≥1000
0
0
0
?
?
?
?
≥1
?
?
?
?
?
23
0
0
0
0
0
0
0
0
0
?
?
?
?
≥1
?
?
?
?
?
24
0
≥1000
0
64
0
≥1000
0
≥100
?
≥1
?
≥1
?
≥1
?
≥1
?
≥1
?
25
0
0
0
0
0
0
?
?
?
?
?
?
?
≥1
?
?
?
?
?
26
0
0
0
0
0
≥1000
?
?
?
?
?
?
?
≥1
?
?
?
?
?
27
0
0
0
0
0
0
?
?
?
?
?
?
?
≥1
?
?
?
?
?
28
0
≥1000
0
0
0
≥1000
?
?
?
≥1
?
?
?
≥1
?
?
?
≥1
?
29
0
0
0
0
0
0
?
?
?
?
?
?
?
≥1
?
?
?
?
?
30
0
0
0
0
0
≥1000
?
?
?
?
?
?
?
≥1
?
?
?
?
?
31
0
0
0
0
0
?
?
?
?
?
?
?
?
≥1
?
?
?
?
?
32
0
≥1000
64
256
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
4k
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Smallest prime reptiles

Smallest prime reptile (8P3x4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
10²
11²
12²
13²
14²
P3 octomino
1
0
0
75008
23632
≥100000
≥100000
≥100000
≥100000
≥100000
≥100000
≥100000
≥100000
≥100000

See Also

P2 octominoA2 9-omino