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 T1 hexomino

Prime rectangles: 4.

Smallest rectangle tilings

Smallest rectangle (3x4):

Smallest square (6x6):

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
N>0
1-2
0
3
0
0
4
0
2
0
5
0
4
0
0
6
0
6
40
100
402
7
0
12
0
0
≥1
0
8
0
26
0
0
≥1
0
0
9
0
48
440
1648
≥1
≥1
≥1
≥1
10
0
84
0
0
≥1
0
0
≥1
0
11
0
152
0
0
≥1
0
0
≥1
0
0
12
0
278
4416
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
496
0
0
≥1
0
0
≥1
0
0
≥1
0
14
0
872
0
0
≥1
0
0
≥1
0
0
≥1
0
0
15
0
1536
42830
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
2708
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
17
0
4748
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
18
0
8286
408452
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
?
20
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
?
N>0
x
all
3k
3k
all
3k
3k
all
3k
3k
all
3k
3k
all
3k
3k
all

Smallest common multiples

Smallest common multiple (area 6):

Common multiples' solutions count (excluding symmetric)

area
6
solutions
1

See Also

I triomino and Z pentominoI triomino and I heptomino