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.


L tetromino and V pentomino

Prime rectangles: 20.

Smallest rectangle tilings

Smallest rectangle (3x6):

Smallest square (5x5):

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
48
6
0
4
0
28
72
7
0
8
0
44
1544
1768
8
0
0
0
24
1064
12750
116100
9
0
0
10
496
14708
198492
1396510
≥1
10
0
0
40
8334
48606
681014
10868204
≥1
≥1
11
0
0
156
5816
360354
7178216
105962514
≥1
≥1
≥1
12
0
16
504
19538
878704
29019828
785086968
≥1
≥1
≥1
≥1
13
0
64
1552
135704
4739620
152849340
6.99721099×10¹⁰
≥1
≥1
≥1
≥1
≥1
14
0
104
4356
166528
20073676
1.27453420×10¹⁰
5.29286132×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
15
0
80
12044
1472120
95190670
5.17659788×10¹⁰
4.45250232×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
0
31634
1560730
350418746
3.21775137×10¹¹
3.43818851×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
0
82048
5739060
1.52492730×10¹⁰
2.25431714×10¹²
2.80959785×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
64
206530
32129394
6.62640527×10¹⁰
1.01002293×10¹³
2.20809418×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
384
515574
48836096
2.88417561×10¹¹
6.75018634×10¹³
1.77984248×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
1024
1261792
287524932
1.15296944×10¹²
4.02146255×10¹⁴
1.41298706×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
1536
3072066
577612504
4.92673772×10¹²
2.02099224×10¹⁵
1.13102034×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
22
0
1360
7381144
1.55246792×10¹⁰
2.08139836×10¹³
1.30647595×10¹⁶
9.01031580×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
23
0
672
17676302
7.33410798×10¹⁰
8.98719598×10¹³
7.35796431×10¹⁶
7.18725376×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
24
0
256
41951594
1.31135805×10¹¹
3.65654432×10¹⁴
3.99030076×10¹⁷
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
25
0
2048
99375034
6.08586518×10¹¹
1.55865096×10¹⁵
2.48162537×10¹⁸
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
all
all
all
all
all
all
all
all
?
?
?
?
?
?
?
?
?
?

See Also

L tetromino and U pentominoL tetromino and W pentomino