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.


Monominoes and O tetromino

Prime rectangles: 4.

Smallest rectangle tilings

Smallest rectangle (2x3):

Smallest square (3x3):

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
1
0
2
0
0
3
0
2
4
4
0
3
10
33
5
0
7
20
92
≥1
6
0
11
42
267
≥1
≥1
7
0
20
84
746
≥1
≥1
≥1
8
0
32
170
2113
≥1
≥1
≥1
≥1
9
0
54
340
5932
≥1
≥1
≥1
≥1
≥1
10
0
87
682
16715
≥1
≥1
≥1
≥1
≥1
≥1
11
0
143
1364
47002
≥1
≥1
≥1
≥1
≥1
≥1
≥1
12
0
231
2730
132289
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
376
5460
372156
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
0
608
10922
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
986
21844
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
1595
43690
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
?
?
?
?

Smallest prime reptiles

Smallest prime reptiles (1Ox3, 4Ox2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
O monomino
?
?
?
?
O tetromino
?
?
?
?

Smallest common multiples

Smallest common multiple (area 4):

Common multiples' solutions count (excluding symmetric)

area
4
solutions
1

See Also

Monominoes and L tetrominoMonominoes and T tetromino