POLYOMINO TILINGS

Polyomino Tilings

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


I pentomino

Area: 5.

Perimeter: 12.

Size: 1x5.

Is rectangular: yes.

Is convex: yes.

Holes: 0.

Order: 1.

Square order: 5.

Odd order: 1.

Prime rectangles: ≥ 1.

Smallest rectangle tilings

Smallest rectangle and smallest odd rectangle (1x5):

Smallest square (5x5):

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
1
1
1
1
2
6
0
0
0
0
3
0
7
0
0
0
0
4
0
0
8
0
0
0
0
5
0
0
0
9
0
0
0
0
6
0
0
0
0
10
1
1
1
1
8
≥1
≥1
≥1
≥1
≥1
11
0
0
0
0
≥1
0
0
0
0
≥1
0
12
0
0
0
0
≥1
0
0
0
0
≥1
0
0
13
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
14
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
15
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
17
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
18
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
19
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
20
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
?
N>0
5k
5k
5k
5k
all
5k
5k
5k
5k
all
?
?
?
?
?
?
?
?
?
?

Smallest prime reptiles

Smallest prime reptile (5Ix2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
1²
2²
3²
4²
5²
6²
I pentomino
1
1
≥1
≥1
≥1
≥1

Smallest tori tilings

Smallest torus and smallest odd torus (1x5):

Smallest square torus (5x5):

Tori tilings' solutions count (including translations)

w \ h
1
2
3
4
5
6
7
8
9
10
1
0
2
0
0
3
0
0
0
4
0
0
0
0
5
5
25
125
625
6250
6
0
0
0
0
15655
0
7
0
0
0
0
78300
0
0
8
0
0
0
0
391625
0
0
0
9
0
0
0
0
≥500000
0
0
0
0
10
5
25
125
625
≥500000
16105
80540
404145
≥500000
≥500000

Smallest Baiocchi figures

Smallest Baiocchi figure (area 20):

Smallest Baiocchi figure without holes (area 25):

See Also

PentominoesL pentomino