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.


I heptomino

Area: 7.

Perimeter: 16.

Size: 1x7.

Is rectangular: yes.

Is convex: yes.

Holes: 0.

Order: 1.

Square order: 7.

Odd order: 1.

Prime rectangles: 1.

Smallest rectangle tilings

Smallest rectangle and smallest odd rectangle (1x7):

Smallest square (7x7):

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
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
1
1
1
1
1
1
2
8
0
0
0
0
0
0
≥1
0
9
0
0
0
0
0
0
≥1
0
0
10
0
0
0
0
0
0
≥1
0
0
0
11
0
0
0
0
0
0
≥1
0
0
0
0
12
0
0
0
0
0
0
≥1
0
0
0
0
0
13
0
0
0
0
0
0
≥1
0
0
0
0
0
0
14
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
0
0
0
0
0
≥1
0
0
0
0
0
0
≥1
?
16
0
0
0
0
0
0
≥1
0
0
0
0
0
0
≥1
?
17
0
0
0
0
0
0
≥1
0
0
0
0
0
0
≥1
?
18
0
0
0
0
0
0
≥1
0
0
0
0
0
0
≥1
?
19
0
0
0
0
0
0
≥1
0
0
0
0
0
0
≥1
?
20
0
0
0
0
0
0
≥1
0
0
0
0
0
0
≥1
?
N>0
7k
7k
7k
7k
7k
7k
all
?
?
?
?
?
?
?

Smallest prime reptiles

Smallest prime reptile (7Ix2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I heptomino
1
1
1
1
1
1

See Also

Y1 hexominoL1 heptomino