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 T tetromino

Prime rectangles: 5.

Smallest rectangle tilings

Smallest rectangle (3x4):

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
1-2
0
3
0
0
4
0
7
28
5
0
0
160
0
6
0
71
696
7501
≥1
7
0
0
2945
0
≥1
0
8
0
539
12035
284470
≥1
≥1
≥1
9
0
0
≥1
0
≥1
0
≥1
0
10
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
11
0
0
≥1
0
≥1
0
≥1
0
≥1
0
12
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
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
15
0
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
17
0
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
19
0
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
N>0
x
2k
all
2k
all
2k
all
2k
?
?
?
?
?
?
?
?
?
?
?

Smallest prime reptiles

Smallest prime reptiles (2Ix3, 4Tx3):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I domino
0
0
71
T tetromino
0
0
22392

Smallest common multiples

Smallest common multiple (area 8):

Common multiples' solutions count (excluding symmetric)

area
4
8
solutions
0
≥2

See Also

Dominoes and O tetrominoDominoes and Z tetromino