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, T tetromino and X pentomino

Prime rectangles: ≥ 47.

Smallest rectangle tilings

Smallest rectangle (5x9):

Smallest square (9x9):

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
0
6
0
0
0
0
0
7
0
0
0
0
0
0
8
0
0
0
0
0
0
0
9
0
0
0
14
0
0
0
29144
10
0
0
0
2
0
10
0
7644
54
11
0
0
0
0
28
412
63
≥1000
≥1000
≥100
12
0
0
0
0
0
4
276
≥1000
≥1000
≥100
≥100
13
0
0
0
784
154
524
≥1000
≥1000
≥1000
≥100
≥100
≥1
14
0
0
0
178
0
≥1000
≥1000
≥1000
≥1000
≥100
≥100
≥1
≥1
15
0
0
0
16
3750
≥1000
≥1000
≥1000
≥1000
≥100
≥100
≥1
≥1
≥1
16
0
0
0
2
46
≥1000
≥1000
≥1000
≥1000
≥100
≥100
≥1
≥1
≥1
≥1
17
0
0
0
29710
24176
≥1000
≥1000
≥1000
≥1000
≥100
≥100
≥1
≥1
≥1
≥1
≥1
18
0
0
0
9844
382
≥1000
≥1000
≥1000
≥1000
≥100
≥100
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
0
1826
337212
≥1000
≥1000
≥1000
≥1000
≥100
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
0
0
312
14288
≥1000
≥1000
≥1000
≥1000
≥100
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
0
957260
≥1000000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
0
0
0
431074
100118
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
23
0
0
0
121172
≥1000000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
24
0
0
0
27122
≥1
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
25
0
0
0
≥1000000
≥1
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
26
0
0
0
≥1000000
≥1
≥1000
≥1000
≥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

Smallest prime reptiles

Smallest prime reptile (4Ix5):

Image Not Found

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
1²
2²
3²
4²
5²
I tetromino
?
?
?
?
?
T tetromino
?
?
?
?
?
X pentomino
?
?
?
?
?

See Also

I triomino, T tetromino and X pentominoI tetromino, X pentomino and Z pentomino