POLYOMINO TILINGS

Polyomino Tilings

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A2 9-omino

Area: 9.

Size: 3x4.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 2.

Square order: 4.

Odd order: ≤ 247.

Prime rectangles: ≥ 16.

Smallest rectangle tilings

Smallest rectangle (3x6):

Smallest square (6x6):

Smallest known odd rectangle (19x117):

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
1-2
0
3
0
0
4-5
0
0
0
6
0
2
0
8
7-8
0
0
0
0
0
9
0
0
0
24
0
0
10
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
12
0
4
0
80
0
704
0
0
9216
13
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
256
0
0
0
0
97280
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
18
0
8
0
832
0
20992
0
0
1150976
0
0
38764544
32
0
1.76370483×10¹⁰
19
0
0
0
0
0
0
0
0
0
0
0
0
0
0
512
0
20
0
0
0
0
0
0
0
0
0
0
0
0
0
0
520
0
?
21
0
0
0
2688
0
0
0
0
12795904
0
0
0
0
0
6.61211095×10¹¹
0
?
?
22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
96256
0
?
?
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8320
0
?
?
24
0
16
0
8704
0
626688
0
0
147128320
0
0
1.55440917×10¹¹
0
0
2.80328834×10¹³
0
?
?
25
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2490880
0
?
?
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1728768
0
?
?
27
0
0
0
28160
0
0
0
0
1.66094438×10¹⁰
0
0
0
4096
0
1.09788907×10¹⁵
0
?
?
28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
212603392
0
?
?
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
43580416
0
?
?
30
0
32
0
91136
0
18710528
0
0
1.89383311×10¹¹
0
0
6.23847446×10¹³
0
0
4.52381753×10¹⁶
0
?
?
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7.23313254×10¹⁰
0
?
?
32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4.00220774×10¹⁰
0
?
?
33
0
0
0
294912
0
0
0
0
2.14769336×10¹²
0
0
0
0
0
1.80404112×10¹⁸
0
?
?
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4.33168864×10¹²
0
?
?
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.32364567×10¹²
0
?
?
36
0
64
0
954368
0
558628864
256
0
2.44277942×10¹³
32768
0
2.50407063×10¹⁶
2.71707750×10¹⁰
237568
7.34699236×10¹⁹
7.91405378×10¹²
≥1
?
37
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.69366536×10¹⁴
0
?
?
38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8.31512029×10¹³
0
?
?
39
0
0
0
3088384
0
0
0
0
2.77395160×10¹⁴
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
40
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8.56126559×10¹⁵
0
?
?
41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3.18922745×10¹⁵
0
?
?
42
0
128
0
9994240
0
1.66786498×10¹¹
0
0
3.15277443×10¹⁵
0
0
1.00513121×10¹⁹
0
0
≥1.84467440×10²⁰
0
?
?
43
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3.56158569×10¹⁷
0
?
?
44
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.65813630×10¹⁷
0
?
?
45
0
0
0
32342016
0
0
0
0
3.58162798×10¹⁶
0
0
0
3.29720012×10¹⁰
0
≥1.84467440×10²⁰
0
?
?
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.65705434×10¹⁹
0
?
?
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6.82874701×10¹⁸
0
?
?
48
0
256
0
104660992
0
4.97964548×10¹²
0
0
4.06986848×10¹⁷
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
49
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
51
0
0
0
338690048
0
0
0
0
4.62401418×10¹⁸
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
52
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
53
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
54
0
512
0
1.09602406×10¹⁰
0
1.48674319×10¹⁴
0
0
5.25401363×10¹⁹
4096
0
≥1.84467440×10²⁰
2.26306361×10¹²
2.81451724×10¹¹
≥1.84467440×10²⁰
1.33762826×10¹⁶
≥1
?
55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
56
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
57
0
0
0
3.54680832×10¹⁰
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
58
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
59
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
60
0
≥1
0
1.14777128×10¹¹
0
4.43888091×10¹⁵
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
61
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
62
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
63
0
0
0
3.71426590×10¹¹
0
0
0
0
≥1.84467440×10²⁰
0
0
0
5.11067137×10¹⁴
0
≥1.84467440×10²⁰
0
?
?
64
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
65
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
66
0
2048
0
1.20196169×10¹²
0
1.32529032×10¹⁷
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
67
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
68
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
69
0
0
0
3.88962975×10¹²
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
70
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
71
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
72
0
4096
0
1.25871063×10¹³
0
3.95684066×10¹⁸
65536
0
≥1.84467440×10²⁰
1.68021196×10¹⁰
50331648
≥1.84467440×10²⁰
8.87488332×10¹⁹
4.52474955×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
73
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
74
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
75
0
0
0
4.07327316×10¹³
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
76
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
77
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
78
0
8192
0
1.31813888×10¹⁴
0
1.18137043×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
79
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
80
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
81
0
0
0
4.26558703×10¹⁴
0
0
0
0
≥1.84467440×10²⁰
0
2.28170137×10¹⁰
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
?
82
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
83
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
84
0
16384
0
1.38037296×10¹⁵
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
85
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
86
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
87
0
0
0
4.46698073×10¹⁵
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
88
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
89
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
90
0
32768
0
1.44554533×10¹⁶
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
2.20620390×10¹⁰
1.17037858×10¹²
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
91
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
92
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
93
0
0
0
4.67788295×10¹⁶
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
94
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
95
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
96
0
65536
0
1.51379472×10¹⁷
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
97
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
98
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
99
0
0
0
4.89874263×10¹⁷
0
0
0
0
≥1.84467440×10²⁰
0
5.45782969×10¹³
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
?
100
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
101
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
102
0
131072
0
1.58526641×10¹⁸
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
103
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
104
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
105
0
0
0
5.13002988×10¹⁸
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
106
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
107
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
108
0
262144
0
1.66011254×10¹⁹
0
≥1.84467440×10²⁰
16777216
0
≥1.84467440×10²⁰
8.73875604×10¹⁴
2.56557723×10¹⁵
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
109
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
110
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
111
0
0
0
5.37223704×10¹⁹
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
112
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
113
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
114
0
524288
0
1.73849242×10²⁰
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
115
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
116
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
117
0
0
0
≥1.84467440×10²⁰
0
0
0
0
≥1.84467440×10²⁰
0
1.18867600×10¹⁷
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
118
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
119
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
120
0
1048576
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
121
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
122
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
123
0
0
0
≥1.84467440×10²⁰
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
124
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
126
0
2097152
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
1.07312791×10¹⁶
5.46310124×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
127
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
128
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
129
0
0
0
≥1.84467440×10²⁰
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
130
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
131
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
132
0
4194304
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
133
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
134
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
135
0
0
0
≥1.84467440×10²⁰
0
0
0
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
136
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
137
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
138
0
8388608
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
139
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
140
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
141
0
0
0
≥1.84467440×10²⁰
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
142
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
143
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
144
0
16777216
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
4.29496729×10¹⁰
0
≥1.84467440×10²⁰
5.14152108×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
145
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
146
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
147
0
0
0
≥1.84467440×10²⁰
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
148
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
149
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
?
?
150
0
33554432
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
?
?
N>0
x
6k
x
3k
x
6k
36k
x
3k
18k
9k
?
9k
?
all
9k
?

Smallest prime reptiles

Smallest prime reptile (9A2x6):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
A2 9-omino
1
0
0
0
0
≥736624640

See Also

P3 octominoB1 9-omino