POLYOMINO TILINGS

Polyomino Tilings

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


P4 heptomino

Area: 7.

Size: 2x4.

Holes: 0.

Order: 2.

Square order: 28.

Odd order: 33.

Prime rectangles: 3.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (14x14):

Smallest odd rectangle (11x21):

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
6
0
16
0
8
0
0
0
0
0
0
44
0
9
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
120
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
328
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
4
0
44
0
320
896
2728
9216
21760
125584
178424
1250656
2892160
15
0
0
0
0
0
0
0
0
0
0
0
0
0
12868368
0
16
0
0
0
0
0
0
2448
0
0
0
0
0
0
32854552
0
0
17
0
0
0
0
0
0
0
0
0
0
0
0
0
123029280
0
0
0
18
0
0
0
0
0
0
6688
0
0
0
0
0
0
423800072
0
0
0
0
19
0
0
0
0
0
0
0
0
0
0
0
0
0
1.16475825×10¹⁰
0
0
0
0
0
20
0
0
0
0
0
0
18272
0
0
0
0
0
0
4.70098205×10¹⁰
0
0
0
0
0
0
21
0
8
0
344
0
6656
0
186272
0
4301888
32
109629642
768
1.34007916×10¹¹
1073048
≥1
≥1
≥1
≥1
≥1
all
22
0
0
0
0
0
0
49920
0
0
0
0
0
0
5.20777576×10¹¹
0
0
0
0
0
0
?
23
0
0
0
0
0
0
0
0
0
0
0
0
0
1.45496252×10¹²
0
0
0
0
0
0
?
24
0
0
0
0
0
0
136384
0
0
0
0
0
0
5.46412651×10¹²
0
0
0
0
0
0
?
25
0
0
0
0
0
0
0
0
0
0
0
0
0
1.70241485×10¹³
0
0
0
0
0
0
?
26
0
0
0
0
0
0
372608
0
0
0
0
0
0
5.61955217×10¹³
0
0
0
0
0
0
?
27
0
0
0
0
0
0
0
0
0
0
0
0
0
1.90220919×10¹⁴
0
0
0
0
0
0
?
28
0
16
0
2736
0
139264
1017984
13183680
98127316
866918912
2.51276246×10¹¹
7.03792621×10¹¹
2.34234160×10¹³
6.13044452×10¹⁴
3.37442594×10¹⁵
≥1
≥1
≥1
≥1
≥1
?
29
0
0
0
0
0
0
0
0
0
0
0
0
0
2.13023322×10¹⁵
0
0
0
0
0
0
?
30
0
0
0
0
0
0
2781184
0
0
0
0
0
0
6.58726233×10¹⁵
0
0
0
0
0
0
?
31
0
0
0
0
0
0
0
0
0
0
0
0
0
2.31854075×10¹⁶
0
0
0
0
0
0
?
32
0
0
0
0
0
0
7598336
0
0
0
0
0
0
7.34042059×10¹⁶
0
0
0
0
0
0
?
33
0
0
0
0
0
0
0
0
0
0
0
0
0
2.48446967×10¹⁷
0
0
0
0
0
0
?
34
0
0
0
0
0
0
20759040
0
0
0
0
0
0
8.09885738×10¹⁷
0
0
0
0
0
0
?
35
0
32
0
21856
0
2916352
0
948071168
0
1.75567440×10¹²
95193512
4.62160664×10¹⁴
6.65362901×10¹²
2.70476326×10¹⁸
1.03574384×10¹⁶
≥1
≥1
≥1
≥1
≥1
?
36
0
0
0
0
0
0
56714752
0
0
0
0
0
0
8.98867963×10¹⁸
0
0
0
0
0
0
?
37
0
0
0
0
0
0
0
0
0
0
0
0
0
2.92258540×10¹⁹
0
0
0
0
0
0
?
38
0
0
0
0
0
0
154947584
0
0
0
0
0
0
9.86765911×10¹⁹
0
0
0
0
0
0
?
39
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
40
0
0
0
0
0
0
423324672
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
41
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
42
0
64
0
174784
0
61079552
1.15654451×10¹⁰
6.87261004×10¹¹
1.04484689×10¹³
3.56141414×10¹⁴
5.29587220×10¹⁶
3.07809779×10¹⁷
4.44002171×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
?
43
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
44
0
0
0
0
0
0
3.15973836×10¹⁰
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
45
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
46
0
0
0
0
0
0
8.63256576×10¹⁰
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
47
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
48
0
0
0
0
0
0
2.35846082×10¹¹
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
49
0
128
0
1398144
0
1.27926272×10¹⁰
0
5.00527989×10¹³
0
7.23021985×10¹⁶
3.84694185×10¹⁴
≥1.84467440×10²⁰
3.69385722×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
?
50
0
0
0
0
0
0
6.44343480×10¹¹
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
51
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
52
0
0
0
0
0
0
1.76037912×10¹²
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
53
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
54
0
0
0
0
0
0
4.80944521×10¹²
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
55
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
56
0
256
0
11184896
0
2.67932139×10¹¹
1.31396486×10¹³
3.65704894×10¹⁵
1.11253995×10¹⁷
1.46870266×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
?
57
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
58
0
0
0
0
0
0
3.58981877×10¹³
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
59
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
60
0
0
0
0
0
0
9.80756729×10¹³
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
61
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
62
0
0
0
0
0
0
2.67947721×10¹⁴
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
63
0
512
0
89478656
0
5.61164320×10¹²
0
2.67883023×10¹⁷
15552
≥1.84467440×10²⁰
1.20208994×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
?
N>0
x
7k
x
7k
x
7k
2k
7k
7k
7k
7k
7k
7k
all
7k
7k
7k
7k
7k
7k

Smallest prime reptiles

Smallest prime reptile (7P4x4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
10²
11²
P4 heptomino
1
0
0
48
0
784
?
≥1
?
≥1
≥1

See Also

P3 heptominoU heptomino