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 heptomino

Area: 7.

Perimeter: 16.

Size: 2x6.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 2.

Square order: 28.

Odd order: 27.

Prime rectangles: 2.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (14x14):

Smallest odd rectangle (9x21):

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
0
0
0
0
7
0
2
0
4
0
8
0
8
0
0
0
0
0
0
16
0
9
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
32
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
64
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
4
0
16
0
64
128
264
1536
1096
10752
4562
≥1000
≥1000
15
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1000
0
16
0
0
0
0
0
0
256
0
0
0
0
0
0
≥1000
0
0
17
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
18
0
0
0
0
0
0
512
0
0
0
0
0
0
≥1000
0
0
0
0
19
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
0
0
20
0
0
0
0
0
0
1024
0
0
0
0
0
0
≥1000
0
0
0
0
0
0
21
0
8
0
64
0
512
0
4352
512
37888
9216
333824
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
?
22
0
0
0
0
0
0
2048
0
0
0
0
0
0
≥1000
0
0
0
0
0
0
?
23
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
0
0
0
?
24
0
0
0
0
0
0
4096
0
0
0
0
0
0
≥1000
0
0
0
0
0
0
?
25
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
0
0
0
?
26
0
0
0
0
0
0
8192
0
0
0
0
0
0
≥1000
0
0
0
0
0
0
?
27
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1000
0
0
0
0
0
0
?
28
0
16
0
256
0
4096
16384
71888
2629696
1315392
124333056
≥143000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
7k
x
7k
x
7k
2k
7k
7k
7k
7k
7k
7k
all
?
?
?
?
?
?

Smallest prime reptiles

Smallest prime reptile (7L1x6):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
L1 heptomino
1
0
0
0
0
12288
1572864
≥1100000

See Also

I heptominoP1 heptomino