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.


I tetromino and U pentomino

Prime rectangles: 66.

Smallest rectangle tilings

Smallest rectangle (6x13):

Smallest square (11x11):

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
1-5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-5
0
6
0
0
7
0
0
0
8
0
0
0
0
9
0
0
0
0
0
10
0
0
0
0
9
0
11
0
0
0
8
0
44
224
12
0
0
0
16
38
112
1909
8216
13
0
2
0
24
8
1562
552
≥1000
≥1000
14
0
0
2
32
453
219
≥1000
≥1000
≥1000
≥1
15
0
0
0
246
40
4676
≥1000
≥1000
≥1000
≥1
≥48000
16
0
2
14
616
2063
17292
≥1000
≥1000
≥1000
≥1
≥1
≥1
17
0
26
4
1170
714
110551
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
18
0
0
50
1953
17418
25059
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
19
0
0
40
6204
3268
310499
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
20
0
30
498
16169
85586
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
246
100
34948
36318
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
0
0
866
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
23
0
4
1384
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
24
0
318
10956
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
25
0
2058
1548
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
26
0
4
12316
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
27
0
84
28036
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
28
0
2866
185842
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
29
0
16062
19736
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
30
0
92
155058
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
31
0
1046
442524
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
32
0
23460
2674034
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
33
0
119868
229252
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
34
0
1292
1810544
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
35
0
10258
6049772
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
36
0
180646
34358230
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
37
0
867478
2543996
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
38
0
14442
20207980
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
39
0
88284
75346064
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
40
0
1335422
406612136
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
x
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all

See Also

I tetromino and T pentominoI tetromino and V pentomino