POLYOMINO TILINGS

Polyomino Tilings

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


T pentomino and W pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (8x10):

Smallest known square (10x10):

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
?
?
?
?
?
6
0
0
0
0
?
0
7
0
0
0
0
0
0
0
8
0
0
0
0
?
0
0
0
9
0
0
0
0
?
0
0
0
0
10
?
?
?
?
?
?
0
2
4
6
11
0
0
0
0
?
0
0
0
0
4
0
12
0
0
0
0
?
0
0
0
0
4
0
0
13
0
0
0
0
?
0
0
0
0
6
0
0
0
14
0
0
0
0
?
0
0
0
0
6
0
0
0
0
15
?
?
?
?
?
?
0
2
0
18
4
26
40
82
376
16
0
0
0
0
?
0
0
0
0
24
0
0
0
0
668
0
17
0
0
0
0
?
0
0
0
0
≥1
0
0
0
0
2096
0
0
18
0
0
0
0
?
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
19
0
0
0
0
?
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
20
?
?
?
?
?
?
0
8
52
≥1
192
574
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
0
0
?
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
?
22
0
0
0
0
?
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
?
23
0
0
0
0
?
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
?
24
0
0
0
0
?
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
?
25
?
?
?
?
?
?
?
18
110
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Smallest prime reptiles

Smallest prime reptiles (5Tx8, 5Wx8):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
1²
2²
3²
4²
5²
6²
7²
8²
9²
T pentomino
0
0
0
0
0
0
0
60
≥1
W pentomino
0
0
0
0
0
0
0
16
≥11000

Smallest common multiples

Smallest common multiple (area 70):

Smallest common multiple without holes (area 80):

Common multiples' solutions count (excluding symmetric)

area
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
solutions
?
?
?
?
?
?
?
?
?
?
?
?
?
≥1
?
≥1

See Also

T pentomino and U pentominoT pentomino and Y pentomino