POLYOMINO TILINGS

Polyomino Tilings

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


P3 heptomino

Area: 7.

Size: 3x3.

Holes: 0.

Order: 28.

Square order: 28.

Odd order: 45.

Prime rectangles: ≥ 37.

Smallest rectangle tilings

Smallest rectangle and smallest square (14x14):

Smallest odd rectangle (15x21):

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
1-10
11
12
13
14
15
16
17
18
19
20
21
N>0
1-10
0
11
0
0
12
0
0
0
13
0
0
0
0
14
0
0
0
0
96
15
0
0
0
0
0
0
16
0
0
0
0
0
0
0
17
0
0
0
0
0
0
0
0
18
0
0
0
0
0
0
0
0
0
19
0
0
0
0
640
0
0
0
0
0
20
0
0
0
0
3104
0
0
0
0
0
0
21
0
0
128
0
0
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
22
0
0
0
0
128
0
0
0
0
0
0
?
?
23
0
0
0
0
1536
0
0
0
0
0
0
?
?
24
0
0
0
0
7680
0
0
0
0
0
0
≥1
?
25
0
0
0
0
38176
0
0
0
0
0
0
?
?
26
0
0
0
0
123168
0
0
0
0
0
0
?
?
27
0
0
0
0
1664
0
0
0
0
0
0
≥1
?
28
0
0
8192
0
39680
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
?
29
0
0
0
0
172160
0
0
0
0
0
0
≥1
?
30
0
0
0
0
606304
0
0
0
0
0
0
≥1
?
31
0
0
0
0
2169536
0
0
0
0
0
0
≥1
?
32
0
0
0
0
5010848
0
0
0
0
0
0
≥1
?
33
0
0
0
0
727168
0
0
0
0
0
0
≥1
?
34
0
0
0
0
4158208
0
0
0
0
0
0
≥1
?
35
0
2048
276736
0
14081440
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
36
0
0
0
0
42337888
0
0
0
0
0
0
≥1
?
37
0
0
0
0
116141280
0
0
0
0
0
0
≥1
?
38
0
0
0
0
215708448
0
0
0
0
0
0
≥1
?
39
0
0
0
0
85071616
0
0
0
0
0
0
≥1
?
40
0
0
0
0
340132448
0
0
0
0
0
0
≥1
?
41
0
0
0
0
1.00919795×10¹⁰
0
0
0
0
0
0
≥1
?
42
0
1152
4366848
0
2.63372787×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
43
0
0
0
0
6.11236249×10¹⁰
0
0
0
0
0
0
≥1
?
44
0
0
0
0
1.00037615×10¹¹
0
0
0
0
0
0
≥1
?
45
0
0
0
0
7.63045814×10¹⁰
0
0
0
0
0
0
≥1
?
46
0
0
0
0
2.50986282×10¹¹
0
0
0
0
0
0
≥1
?
47
0
0
0
0
6.66477827×10¹¹
0
0
0
0
0
0
≥1
?
48
0
0
0
0
1.56105462×10¹²
0
0
0
0
0
0
≥1
?
49
0
61440
177596928
0
3.23486470×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
50
0
0
0
0
5.07339950×10¹²
0
0
0
0
0
0
≥1
?
51
0
0
0
0
5.97595227×10¹²
0
0
0
0
0
0
≥1
?
52
0
0
0
0
1.72219158×10¹³
0
0
0
0
0
0
≥1
?
53
0
0
0
0
4.18563564×10¹³
0
0
0
0
0
0
≥1
?
54
0
0
0
0
9.04421722×10¹³
0
0
0
0
0
0
≥1
?
55
0
0
0
0
1.74963655×10¹⁴
0
0
0
0
0
0
≥1
?
56
0
64512
4.07731724×10¹⁰
0
2.79531547×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
57
0
0
0
0
4.31138013×10¹⁴
0
0
0
0
0
0
≥1
?
58
0
0
0
0
1.12611669×10¹⁵
0
0
0
0
0
0
≥1
?
59
0
0
0
0
2.55178305×10¹⁵
0
0
0
0
0
0
≥1
?
60
0
0
0
0
5.20972878×10¹⁵
0
0
0
0
0
0
≥1
?
61
0
0
0
0
9.74800176×10¹⁵
0
0
0
0
0
0
≥1
?
62
0
0
0
0
1.63659356×10¹⁶
0
0
0
0
0
0
≥1
?
63
0
1107968
1.33008183×10¹²
0
2.94359781×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
64
0
0
0
0
7.12732295×10¹⁶
0
0
0
0
0
0
≥1
?
65
0
0
0
0
1.53073145×10¹⁷
0
0
0
0
0
0
≥1
?
66
0
0
0
0
3.01462696×10¹⁷
0
0
0
0
0
0
≥1
?
67
0
0
0
0
5.59706196×10¹⁷
0
0
0
0
0
0
≥1
?
68
0
0
0
0
9.93239360×10¹⁷
0
0
0
0
0
0
≥1
?
69
0
0
0
0
1.93422722×10¹⁸
0
0
0
0
0
0
≥1
?
70
0
9185280
4.16378133×10¹³
0
4.41538784×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
7k
7k
x
all
7k
7k
7k
7k
7k
7k
all

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
P3 heptomino
1
0
0
0
0
0
0

See Also

P2 heptominoP4 heptomino