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.


Dominoes and I tetromino

Prime rectangles: 7.

Smallest rectangle tilings

Smallest rectangle (1x6):

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
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
0
2
0
0
3
0
0
0
4
0
2
14
108
5
0
6
0
490
0
6
2
17
146
2539
22183
≥1
7
0
34
0
10994
0
≥1
0
8
3
80
1269
52483
≥1
≥1
≥1
≥1
9
0
165
0
≥1
0
≥1
0
≥1
0
10
7
358
10171
≥1
≥1
≥1
≥1
≥1
≥1
≥1
11
0
724
0
≥1
0
≥1
0
≥1
0
≥1
0
12
11
1508
79393
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
3039
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
14
20
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
16
32
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
18
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
20
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
2k
all
2k
all
2k
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Smallest prime reptiles

Smallest prime reptiles (2Ix2, 4Ix2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I domino
?
?
?
?
I tetromino
?
?
?
?

Smallest common multiples

Smallest common multiple (area 4):

Common multiples' solutions count (excluding symmetric)

area
4
solutions
1

See Also

Dominoes and L triominoDominoes and L tetromino