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.


L1 12-omino

Area: 12.

Perimeter: 18.

Size: 3x6.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 8.

Square order: 12.

Prime rectangles: ≥ 2.

Smallest rectangle tilings

Smallest rectangle (8x12):

Smallest square (12x12):

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
1-7
8
9-11
12
13-15
16
17-19
20
21-23
24
N>0
1-7
0
8
0
0
9-11
0
0
0
12
0
2
0
2
13-15
0
0
0
0
0
16
0
0
0
6
0
0
17-19
0
0
0
0
0
0
0
20
0
0
0
10
0
0
0
0
21-23
0
0
0
0
0
0
0
0
0
24
0
4
0
22
0
40
0
302
0
1260
25
0
0
0
0
0
0
0
0
0
0
?
26
0
0
0
0
0
0
0
0
0
0
?
27
0
0
0
0
0
0
0
0
0
0
?
28
0
0
0
42
0
0
0
0
0
4958
?
29
0
0
0
0
0
0
0
0
0
0
?
30
0
0
0
0
0
0
0
0
0
0
?
31
0
0
0
0
0
0
0
0
0
0
?
32
0
0
0
86
0
0
0
0
0
24844
?
33
0
0
0
0
0
0
0
0
0
0
?
34
0
0
0
0
0
0
0
0
0
0
?
35
0
0
0
0
0
0
0
0
0
0
?
36
0
8
0
170
0
272
0
7578
0
107350
?
37
0
0
0
0
0
0
0
0
0
0
?
38
0
0
0
0
0
0
0
0
0
0
?
39
0
0
0
0
0
0
0
0
0
0
?
40
0
0
0
342
0
0
0
0
0
477548
?
41
0
0
0
0
0
0
0
0
0
0
?
42
0
0
0
0
0
0
0
0
0
0
?
43
0
0
0
0
0
0
0
0
0
0
?
44
0
0
0
682
0
0
0
0
0
2190158
?
45
0
0
0
0
0
0
0
0
0
0
?
46
0
0
0
0
0
0
0
0
0
0
?
47
0
0
0
0
0
0
0
0
0
0
?
48
0
16
0
1366
0
1856
0
194174
0
9736428
?
N>0
x
12k
x
?
x
?
x
?
x
?

Smallest prime reptiles

Smallest prime reptile (12L1x12):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
10²
11²
12²
13²
14²
15²
L1 12-omino
≥1
0
0
0
0
0
0
0
0
0
0
≥4000000
0
0
0

See Also

P1 11-ominoO1 12-omino