POLYOMINO TILINGS

Polyomino Tilings

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


I hexomino and T1 hexomino

Prime rectangles: 24.

Smallest rectangle tilings

Smallest rectangle (3x8):

Smallest square (12x12):

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
0
0
0
5
0
0
0
0
6
0
0
0
0
0
7
0
0
0
0
0
0
8
0
1
0
0
1
0
0
9
0
0
0
0
2
0
13
0
10
0
0
0
0
3
0
0
2
0
11
0
0
0
0
4
0
0
0
0
0
12
0
0
0
0
5
10
37
70
109
154
412
13
0
0
0
0
6
0
0
0
0
0
841
0
14
0
3
0
0
16
0
0
387
0
0
3907
0
0
15
0
0
0
0
28
0
184
0
102
0
8730
0
≥1000
0
16
0
1
0
0
43
0
0
359
0
0
16569
0
0
≥1000
0
17
0
0
0
0
61
0
0
0
0
0
28173
0
0
0
0
0
18
0
0
0
0
82
194
723
1630
2889
4546
51285
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
19
0
0
0
0
106
0
0
0
0
0
92214
0
0
0
0
0
≥1000
0
20
0
6
0
0
169
0
0
9678
0
0
312288
0
0
≥1000
0
0
≥1000
0
0
21
0
0
2
0
255
0
2851
0
8846
0
744235
0
≥1000
0
≥1000
0
≥1000
0
≥1
2k
22
0
5
0
0
392
0
0
16571
0
0
≥1
0
0
≥1000
0
0
≥1000
0
0
3k
23
0
0
0
0
578
0
0
0
0
0
≥1
0
0
0
0
0
≥1000
0
0
6k
24
0
1
2
3
824
2426
11556
41320
92793
194492
≥1
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
all
25
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
6k
26
0
10
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
27
0
0
14
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
2k
28
0
15
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
29
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
6k
30
0
7
14
21
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
31
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
6k
32
0
16
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
33
0
0
56
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
2k
34
0
35
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
35
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
6k
36
0
28
56
88
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
37
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
6k
38
0
30
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
39
0
0
168
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
2k
40
0
71
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
41
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
6k
42
0
84
172
312
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
43
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
6k
44
0
73
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
45
0
0
428
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
2k
46
0
137
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
47
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
0
0
0
≥1
0
0
6k
48
0
211
476
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
x
2k
3k
6k
all
6k
3k
2k
3k
6k
all
6k
3k
2k
3k
6k
all
6k
3k

Smallest common multiples

Smallest known common multiple (area 24):

Common multiples' solutions count (excluding symmetric)

area
6
12
18
24
solutions
?
?
?
≥2

See Also

C hexomino and I hexominoT1 hexomino and O1 24-omino