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 W pentomino

Prime rectangles: 30.

Smallest rectangle tilings

Smallest rectangle (4x7):

Smallest square (7x7):

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
1-3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1-3
0
4
0
0
5
0
0
0
6
0
0
0
0
7
0
2
0
0
100
8
0
0
2
0
40
222
9
0
0
0
2
40
344
2428
10
0
22
12
16
3588
6110
16382
≥400000
11
0
4
34
68
≥1
15812
93554
≥1
≥1
12
0
0
8
200
≥1
42012
481484
≥1
≥1
≥1
13
0
160
202
708
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
0
58
382
2514
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
8
218
6994
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
984
2240
20188
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
524
3638
62084
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
144
3348
169648
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
5564
20892
458392
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
3838
32070
≥370000
≥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
all
all

See Also

I triomino and V pentominoI triomino and X pentomino