POLYOMINO TILINGS

Polyomino Tilings

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You may also see list of all polyomino sets for which data is available here.


Dominoes and L tetromino

Prime rectangles: 3.

Smallest rectangle tilings

Smallest rectangle (2x3):

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
4
0
4
0
8
92
624
5
0
24
0
4680
0
6
0
66
1328
32433
≥1
≥1
7
0
≥1
0
≥1
0
≥1
0
8
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
9
0
≥1
0
≥1
0
≥1
0
≥1
0
10
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
11
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
12
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
14
0
≥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
0
≥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
0
≥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
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
all
2k
all
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Smallest prime reptiles

Smallest prime reptiles (2Ix2, 4Lx2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I domino
0
8
1328
L tetromino
0
365
3490752

Smallest common multiples

Smallest common multiple (area 4):

Common multiples' solutions count (excluding symmetric)

area
4
solutions
1

See Also

Dominoes and I tetrominoDominoes and O tetromino