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.


P1 heptomino

Area: 7.

Size: 2x5.

Holes: 0.

Order: 2.

Square order: 28.

Odd order: ≤ 57.

Prime rectangles: ≥ 3.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (14x14):

Smallest known odd rectangle (19x21):

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
0
0
0
0
0
6
0
0
0
0
0
0
7
0
2
0
4
0
10
0
8
0
0
0
0
0
0
32
0
9
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
88
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
228
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
4
0
16
0
100
600
1152
4832
8772
29728
58968
213664
817344
15
0
0
0
0
0
0
0
0
0
0
0
0
0
≥10000
0
16
0
0
0
0
0
0
1632
0
0
0
0
0
0
≥10000
0
?
17
0
0
0
0
0
0
0
0
0
0
0
0
0
≥10000
0
?
?
18
0
0
0
0
0
0
4424
0
0
0
0
0
0
≥10000
0
?
?
?
19
0
0
0
0
0
0
0
0
0
0
0
0
0
≥10000
0
?
?
?
?
20
0
0
0
0
0
0
11872
0
0
0
0
0
0
≥10000
0
?
?
?
?
?
21
0
8
0
64
0
1000
0
43008
0
895616
0
15608768
0
≥10000
?
≥1
?
≥1
≥1
≥1
?
22
0
0
0
0
0
0
31808
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
23
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
24
0
0
0
0
0
0
85520
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
25
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
26
0
0
0
0
0
0
230176
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
27
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
28
0
16
0
256
0
10000
618944
1622016
31902208
91830800
1.17074892×10¹⁰
4.15324598×10¹⁰
6.05523824×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
29
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
30
0
0
0
0
0
0
1663392
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
31
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
32
0
0
0
0
0
0
4471296
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
33
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
34
0
0
0
0
0
0
12021888
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
35
0
32
0
1024
0
100000
0
61341696
0
9.42283123×10¹⁰
0
1.10679123×10¹³
121176064
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
36
0
0
0
0
0
0
32322112
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
37
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
38
0
0
0
0
0
0
86893952
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
39
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
40
0
0
0
0
0
0
233602048
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
41
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
42
0
64
0
4096
0
1000000
628023424
2.32154726×10¹⁰
2.09356900×10¹²
9.67017607×10¹²
4.80269756×10¹⁴
2.95100303×10¹⁵
1.79359185×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
43
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
44
0
0
0
0
0
0
1.68841164×10¹⁰
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
45
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
46
0
0
0
0
0
0
4.53917900×10¹⁰
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
47
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
48
0
0
0
0
0
0
1.22032212×10¹¹
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
49
0
128
0
16384
0
10000000
0
8.78790574×10¹¹
0
9.92428569×10¹⁴
330301440
7.86967688×10¹⁷
9.71336648×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
50
0
0
0
0
0
0
3.28074531×10¹¹
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
51
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
52
0
0
0
0
0
0
8.82005575×10¹¹
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
53
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
54
0
0
0
0
0
0
2.37120989×10¹²
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
55
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1
?
?
?
?
?
?
?
56
0
256
0
65536
0
100000000
6.37482655×10¹²
3.32672060×10¹³
1.37407602×10¹⁶
1.01851365×10¹⁷
2.03496101×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
7k
x
7k
x
7k
2k
7k
?
7k
7k
7k
7k
?
?
?
?
?
?
?

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
P1 heptomino
1
0
0
0
0
0

Attributions

  1. Prime rectangles list taken from http://www.cflmath.com/~reid/Polyomino/7omino2_rect.html

See Also

L1 heptominoP2 heptomino