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.


N pentomino and I2 octomino

Prime rectangles: ≥ 91.

Smallest rectangle tilings

Smallest rectangle and smallest square (16x16):

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
1-9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-9
0
10
0
0
11
0
0
0
12
0
0
0
0
13
0
0
0
0
0
14
0
0
0
0
0
0
15
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
16
17
0
0
0
0
0
0
0
?
?
18
0
0
0
0
0
0
0
?
?
?
19
0
0
0
0
0
0
?
?
?
?
?
20
0
0
0
0
0
?
?
?
?
?
?
?
21
0
0
0
0
0
?
?
?
?
?
?
?
?
22
0
0
0
0
0
?
?
?
?
?
?
?
?
23
0
0
0
2
0
?
?
?
?
?
?
?
?
24
0
0
0
0
0
?
?
?
?
?
?
?
?
25
0
0
0
8
0
?
?
?
?
?
?
?
?
26
0
0
0
2
0
?
?
?
?
?
?
?
?
27
0
0
0
98
0
?
?
?
?
?
?
?
?
28
0
0
0
8
0
?
?
?
?
?
?
?
?
29
0
0
0
478
0
?
?
?
?
?
?
?
?
30
0
0
0
108
0
?
?
?
?
?
?
?
?
31
0
0
0
3654
0
?
?
?
?
?
?
?
?
32
0
0
0
522
0
?
?
≥1
?
?
?
?
?
33
0
0
0
19378
0
?
?
?
?
?
?
?
?
34
0
0
0
4440
0
?
?
?
?
?
?
?
?
35
0
2
0
123354
0
?
?
?
?
?
?
≥1
?
36
0
2
0
22912
64
?
?
?
?
?
?
≥1
?
37
0
0
0
673016
128
?
?
?
?
?
?
?
?
38
0
0
0
158000
42
?
?
?
?
?
?
?
?
39
0
48
0
3943402
0
?
?
?
?
?
?
≥1
?
40
0
78
0
844256
714
?
?
?
?
?
?
≥1
?
41
0
0
0
21601278
32
?
?
?
?
?
?
?
?
42
0
0
0
5180654
288
?
?
?
?
?
?
?
?
43
0
856
0
121436894
144
?
?
?
?
?
?
≥1
?
44
0
1886
0
28132594
1522
?
?
?
?
?
?
≥1
?
45
0
0
0
661990880
6956
?
?
?
?
?
?
?
?
46
0
0
0
162250520
7728
?
?
?
?
?
?
?
?
47
0
13856
0
3.63708794×10¹⁰
9920
?
?
?
?
?
?
≥1
?
48
0
36526
0
883016138
13634
?
?
≥1
?
?
?
≥1
?
49
0
2
0
1.96832445×10¹¹
27200
?
?
?
?
?
?
≥1
?
50
0
2
0
4.92187094×10¹⁰
76724
?
?
?
?
?
?
≥1
?
51
0
212288
0
1.06631067×10¹²
44240
?
?
?
?
?
?
≥1
?
52
0
626838
0
2.68040183×10¹¹
241384
?
?
?
?
?
?
≥1
?
53
0
124
0
5.72946812×10¹²
254176
?
?
?
?
?
?
≥1
?
54
0
96
0
1.46183362×10¹²
617724
?
?
?
?
?
?
≥1
?
55
0
3143924
0
3.07438497×10¹³
743476
?
?
?
?
?
?
≥1
?
56
0
10010572
0
7.89753614×10¹²
1312672
?
?
?
?
?
?
≥1
?
57
0
3902
0
1.64150436×10¹⁴
3139092
?
?
?
?
?
?
≥1
?
58
0
2980
0
4.25887071×10¹³
7016696
?
?
?
?
?
?
≥1
?
59
0
45469600
0
8.74689066×10¹⁴
12047176
?
?
?
?
?
?
≥1
?
60
0
152645328
0
2.28382887×10¹⁴
21671152
?
?
?
?
?
?
≥1
?
61
0
89920
0
4.64516285×10¹⁵
36311468
?
?
?
?
?
?
≥1
?
62
0
69794
0
1.22185284×10¹⁵
77370316
?
?
?
?
?
?
≥1
?
63
0
646045550
0
2.46186309×10¹⁶
164161500
?
?
?
?
?
?
≥1
?
64
0
2.25493809×10¹⁰
0
6.51126205×10¹⁵
263849584
?
?
≥1
?
?
?
≥1
?
65
0
1732164
0
1.30149278×10¹⁷
461105160
?
?
?
?
?
?
≥1
?
66
0
1361606
0
3.46200947×10¹⁶
871200036
?
?
?
?
?
?
≥1
?
67
0
9.05335743×10¹⁰
0
6.86770946×10¹⁷
1.84125495×10¹⁰
?
?
?
?
?
?
≥1
?
68
0
3.25550388×10¹¹
0
1.83546586×10¹⁷
3.51880009×10¹⁰
?
?
?
?
?
?
≥1
?
69
0
29894278
0
3.61680954×10¹⁸
5.88820404×10¹⁰
?
?
?
?
?
?
≥1
?
70
0
23690876
0
9.71106011×10¹⁷
1.08707022×10¹¹
?
?
?
?
?
?
≥1
?
71
0
1.25474401×10¹²
0
1.90163677×10¹⁹
2.09380334×10¹¹
?
?
?
?
?
?
≥1
?
72
0
4.61929463×10¹²
0
5.12654467×10¹⁸
4.21686306×10¹¹
?
?
?
?
?
?
≥1
?
73
0
480824630
0
9.98216442×10¹⁹
7.71190810×10¹¹
?
?
?
?
?
?
≥1
?
74
0
383072162
0
2.70139573×10¹⁹
1.36414193×10¹²
?
?
?
?
?
?
≥1
?
75
0
1.72333684×10¹³
0
5.23240156×10²⁰
2.57124050×10¹²
?
?
?
?
?
?
≥1
?
76
0
6.46630063×10¹³
0
1.42092397×10²⁰
4.99176035×10¹²
?
?
?
?
?
?
≥1
?
77
0
7.37723376×10¹⁰
0
2.73893309×10²¹
9.62125932×10¹²
?
?
?
?
?
?
≥1
?
78
0
5.89900890×10¹⁰
0
7.46219067×10²⁰
1.74575955×10¹³
?
?
?
?
?
?
≥1
?
79
0
2.34913837×10¹⁴
0
1.43192489×10²²
3.18476341×10¹³
?
?
?
?
?
?
≥1
?
80
0
8.95408830×10¹⁴
0
3.91296752×10²¹
6.05711161×10¹³
?
?
≥1
?
?
?
≥1
?
81
0
1.09514803×10¹²
0
7.47731549×10²²
1.16686380×10¹⁴
?
?
?
?
?
?
≥1
?
82
0
8.78050336×10¹¹
0
2.04904539×10²²
2.19151237×10¹⁴
?
?
?
?
?
?
≥1
?
83
0
3.18180640×10¹⁵
0
3.90028751×10²³
3.99855128×10¹⁴
?
?
?
?
?
?
≥1
?
84
0
1.22891325×10¹⁶
0
1.07160699×10²³
7.44910645×10¹⁴
?
?
?
?
?
?
≥1
?
85
0
1.58714666×10¹³
0
2.03235473×10²⁴
1.41570484×10¹⁵
?
?
?
?
?
?
≥1
?
86
0
1.27509870×10¹³
0
5.59760152×10²³
2.69754422×10¹⁵
?
?
?
?
?
?
≥1
?
87
0
4.28609024×10¹⁶
0
1.05799593×10²⁵
5.00914111×10¹⁵
?
?
?
?
?
?
≥1
?
88
0
1.67414952×10¹⁷
0
2.92066180×10²⁴
9.25040597×10¹⁵
?
?
?
?
?
?
≥1
?
89
0
2.25881596×10¹⁴
0
5.50267049×10²⁵
1.73787783×10¹⁶
?
?
?
?
?
?
≥1
?
90
0
1.81758125×10¹⁴
0
1.52232297×10²⁵
3.29421002×10¹⁶
?
?
?
?
?
?
≥1
?
91
0
5.74629504×10¹⁷
0
2.85951069×10²⁶
6.21069305×10¹⁶
?
?
?
?
?
?
≥1
?
92
0
2.26638112×10¹⁸
0
7.92693067×10²⁵
1.15252877×10¹⁷
?
?
?
?
?
?
≥1
?
93
0
3.16960904×10¹⁵
0
1.48476893×10²⁷
2.14700398×10¹⁷
?
?
?
?
?
?
≥1
?
94
0
2.55367754×10¹⁵
0
4.12384743×10²⁶
4.04370691×10¹⁷
?
?
?
?
?
?
≥1
?
95
0
7.67204101×10¹⁸
0
7.70361327×10²⁷
7.63366177×10¹⁷
?
?
?
?
?
?
≥1
?
96
0
3.05158214×10¹⁹
0
2.14349300×10²⁷
1.43097474×10¹⁸
?
?
≥1
?
?
?
≥1
?
97
0
4.39766130×10¹⁶
0
3.99407186×10²⁸
2.66278839×10¹⁸
?
?
?
?
?
?
≥1
?
98
0
3.54672377×10¹⁶
0
1.11323090×10²⁸
4.98545656×10¹⁸
?
?
?
?
?
?
≥1
?
99
0
1.02056872×10²⁰
0
2.06937634×10²⁹
9.38726015×10¹⁸
?
?
?
?
?
?
≥1
?
100
0
4.08960449×10²⁰
0
5.77712093×10²⁸
1.76581034×10¹⁹
?
?
?
?
?
?
≥1
?
N>0
x
all
x
all
all
?
?
?
?
?
?
?

See Also

N pentomino and Y2 hexominoP pentomino and R pentomino