POLYOMINO TILINGS

Polyomino Tilings

Select polyominoes for a set (currently 1 or 2), for which tilings should be shown.

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


B hexomino

Area: 6.

Size: 3x3.

Holes: 0.

Order: 18.

Square order: 96.

Odd order: ∞.

Prime rectangles: ≥ 26.

Smallest rectangle tilings

Smallest rectangle (9x12):

Smallest square (24x24):

No odd rectangles exist.

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
1-8
9
10-11
12
13
14
15
16
17
18
19
20
21
22
23
24
N>0
1-8
0
9
0
0
10-11
0
0
0
12
0
2
0
0
13
0
0
0
2
0
14
0
0
0
2
0
0
15
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
17
0
0
0
2
0
0
0
0
0
18
0
0
0
10
0
0
0
2
0
0
19
0
0
0
2
0
0
0
0
0
0
0
20
0
2
0
0
0
0
0
0
0
24
0
0
21
0
0
0
2
0
0
0
0
0
0
0
46
0
22
0
0
0
20
0
0
0
0
0
0
0
0
0
0
23
0
0
0
18
0
0
0
0
0
0
0
0
0
0
0
24
0
4
0
2
18
6
0
0
80
414
90
252
≥1
≥1
≥1
≥1
25
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
26
0
0
0
36
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
27
0
0
0
70
0
0
0
36
0
0
0
≥48
0
0
0
≥1
4k
28
0
2
0
26
0
0
8
0
0
≥1
0
0
≥1
0
0
≥1
3k
29
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
30
0
0
0
62
0
0
0
356
0
0
0
≥1
0
0
0
≥1
4k
31
0
0
0
182
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
32
0
8
0
152
0
0
34
0
0
≥1
0
0
≥1
0
0
≥1
3k
33
0
0
0
36
0
0
0
998
0
0
0
≥1
0
0
0
≥1
4k
34
0
0
0
104
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
35
0
0
0
412
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
36
0
10
0
568
266
150
284
6562
83436
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
37
0
0
0
276
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
38
0
0
0
214
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
39
0
0
0
862
0
0
0
37524
0
0
0
≥1
0
0
0
≥1
4k
40
0
12
0
1664
0
0
2188
0
0
≥1
0
0
≥1
0
0
≥1
3k
41
0
0
0
1356
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
42
0
0
0
730
0
0
0
198484
0
0
0
≥1
0
0
0
≥1
4k
43
0
0
0
1758
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
44
0
26
0
4278
0
0
14738
0
0
≥1
0
0
≥1
0
0
≥1
3k
45
0
0
0
5016
0
0
0
1062752
0
0
0
≥1
0
0
0
≥1
4k
46
0
0
0
3240
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
47
0
0
0
3958
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
48
0
32
0
10158
6784
18554
95562
5852252
103132102
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
49
0
0
0
15602
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
50
0
0
0
13338
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
51
0
0
0
11272
0
0
0
32540896
0
0
0
≥1
0
0
0
≥1
4k
52
0
50
0
23434
0
0
626236
0
0
≥1
0
0
≥1
0
0
≥1
3k
53
0
0
0
43354
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
54
0
0
0
47738
0
0
0
180078866
0
0
0
≥1
0
0
0
≥1
4k
55
0
0
0
38998
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
56
0
84
0
56604
0
0
4052868
0
0
≥1
0
0
≥1
0
0
≥1
3k
57
0
0
0
112026
0
0
0
996102262
0
0
0
≥1
0
0
0
≥1
4k
58
0
0
0
151806
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
59
0
0
0
140180
0
0
0
0
0
0
0
0
0
0
0
≥1
12k
60
0
114
0
153980
230104
3024338
26184442
5.52334895×10¹⁰
1.30027588×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
x
4k
x
all
12k
12k
4k
3k
12k
4k
12k
3k
4k
12k
12k
all

Smallest prime reptiles

Smallest prime reptile (6Bx9):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
10²
11²
12²
13²
14²
15²
B hexomino
1
0
0
0
0
0
0
0
36
0
0
≥1
≥1
≥1
≥1

Smallest tori tilings

Smallest torus (3x4):

Smallest square torus (6x6):

Smallest odd torus (3x6):

Tori tilings' solutions count (including translations)

w \ h
1
2
3
4
5
6
7
8
9
10
11
12
1
0
2
0
0
3
0
0
0
4
0
0
48
0
5
0
0
0
0
0
6
0
0
24
288
120
432
7
0
0
0
0
0
0
0
8
0
0
216
0
0
≥1000
0
0
9
0
0
0
≥1000
0
240
0
≥1000
0
10
0
0
120
0
0
≥1000
0
0
≥1000
0
11
0
0
0
0
0
528
0
0
0
0
0
12
0
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
13
0
0
0
0
0
≥1000
0
0
0
0
0
≥1000
14
0
0
504
0
0
≥1000
0
0
≥1000
0
0
≥1000
15
0
0
0
≥1000
0
≥1000
0
≥1000
0
≥1000
0
≥1000
16
0
0
≥1000
0
0
≥1000
0
0
≥1000
0
0
≥1000
17
0
0
0
0
0
≥1000
0
0
0
0
0
≥1000
18
0
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
19
0
0
0
0
0
≥1000
0
0
0
0
0
≥1000
20
0
0
≥1000
0
0
≥1000
0
0
≥1000
0
0
≥1000
21
0
0
0
≥1000
0
≥1000
0
≥1000
0
≥1000
0
≥1000
22
0
0
≥1000
0
0
≥1000
0
0
≥1000
0
0
≥1000
23
0
0
0
0
0
≥1000
0
0
0
0
0
≥1000
24
0
0
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000

Attributions

  1. Prime rectangles taken from here http://www2.stetson.edu/~efriedma/order/index.html and here http://www.cflmath.com/~reid/Polyomino/g6_rect.html

See Also

A hexominoC hexomino