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 triomino and O tetromino

Prime rectangles: ≥ 14.

Smallest rectangle tilings

Smallest rectangle (2x5):

Smallest square (4x4):

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
0
2
0
0
3
0
0
0
4
0
0
0
2
5
0
2
0
8
28
6
0
0
2
7
43
202
7
0
3
4
31
170
649
2744
8
0
3
6
69
456
2208
12343
66652
9
0
4
16
108
1056
8624
52796
≥1
≥1
10
0
6
30
285
3068
27987
≥1
≥1
≥1
≥1
11
0
9
48
615
8016
92297
≥1
≥1
≥1
≥1
≥1
12
0
10
94
1101
20364
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
16
168
2548
54696
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
0
20
276
5352
142908
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
27
492
10256
370884
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
36
854
22319
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
49
1416
46349
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
63
2430
91770
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
86
4140
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
113
6878
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
150
11592
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
0
199
19512
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
23
0
265
32392
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
24
0
349
54080
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
25
0
465
90320
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
26
0
615
149706
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
27
0
815
248624
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
28
0
1080
413134
≥1
≥1
≥1
≥1
≥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
all
all
all
all

Smallest prime reptiles

Smallest prime reptiles (3Ix3, 4Ox2):

Image Not FoundImage Not Found

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
1²
2²
3²
4²
5²
I triomino
?
?
?
?
?
O tetromino
?
?
?
?
?

Smallest common multiples

Smallest common multiple (area 12):

Common multiples' solutions count (excluding symmetric)

area
12
solutions
≥1

See Also

I triomino and L tetrominoI triomino and T tetromino