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.


O tetromino and T pentomino

Prime rectangles: ≥ 21.

Smallest rectangle tilings

Smallest rectangle (8x10):

Smallest square (10x10):

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
1-7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-7
0
8
0
0
9
0
0
0
10
0
1
0
4
11
0
0
0
0
0
12
0
2
0
13
0
36
13
0
0
0
0
0
17
0
14
0
3
0
26
0
71
0
156
15
0
0
0
0
0
88
0
0
0
16
0
5
0
58
0
263
0
1074
0
7616
17
0
0
0
0
0
213
0
0
0
0
0
18
0
7
0
142
10
881
626
4122
9518
46060
80546
≥1
19
0
0
0
0
0
1203
0
0
0
0
0
≥1
?
20
0
10
0
298
0
2079
0
13771
0
295160
0
≥1
?
≥1
21
0
0
0
0
0
4551
0
0
0
0
0
≥1
?
?
?
22
0
15
0
694
0
8936
0
95743
0
2109603
0
≥1
?
≥1
?
23
0
0
0
0
0
10842
0
0
0
0
0
≥1
?
?
?
24
0
21
0
1769
380
31654
39445
412040
1382704
13435954
40660015
≥1
≥1
≥1
?
25
0
0
0
0
0
49001
0
0
0
0
0
≥1
?
?
?
26
0
30
0
3956
0
77264
0
1583581
0
88287707
0
≥1
?
≥1
?
27
0
0
0
0
0
180518
0
0
0
0
0
≥1
?
?
?
28
0
43
0
9345
0
319052
0
9805814
0
613306278
0
≥1
?
≥1
?
29
0
0
0
0
0
457392
0
0
0
0
0
≥1
?
?
?
30
0
60
0
23522
9504
1140795
2554050
44773115
214990670
4.01549223×10¹⁰
2.14695253×10¹¹
≥1
≥1
≥1
?
31
0
0
0
0
0
1897639
0
0
0
0
0
≥1
?
?
?
32
0
85
0
54232
0
2946988
0
187901730
0
2.65951667×10¹¹
0
≥1
?
≥1
?
33
0
0
0
0
0
6830315
0
0
0
0
0
≥1
?
?
?
34
0
120
0
128846
0
11825220
0
1.05793789×10¹⁰
0
1.81460242×10¹²
0
≥1
?
≥1
?
35
0
0
0
0
0
18071861
0
0
0
0
0
≥1
?
?
?
36
0
168
0
320512
232392
42160826
164100519
4.95989327×10¹⁰
3.40464966×10¹¹
1.20479350×10¹³
1.15242168×10¹⁴
≥1
≥1
≥1
?
37
0
0
0
0
0
71753430
0
0
0
0
0
≥1
?
?
?
38
0
237
0
752826
0
113635104
0
2.20319815×10¹¹
0
8.02342934×10¹³
0
≥1
?
≥1
?
39
0
0
0
0
0
255975851
0
0
0
0
0
≥1
?
?
?
40
0
333
0
1794569
0
442151618
0
1.16868245×10¹²
0
5.42263924×10¹⁴
0
≥1
?
≥1
?
N>0
x
?
x
?
?
?
?
?
?
?
?
?
?
?

See Also

O tetromino and P pentominoO tetromino and V pentomino