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 I pentomino

Prime rectangles: 20.

Smallest rectangle tilings

Smallest rectangle (1x8):

Smallest square (5x5):

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
0
5
0
0
0
8
24
6
0
0
2
4
46
208
7
0
0
3
4
132
471
660
8
2
4
12
100
530
2712
12564
≥1
9
0
0
23
58
1161
9567
35442
≥1
≥1
10
0
0
36
202
2848
29396
132684
≥1
≥1
≥1
11
3
9
81
921
10100
125677
1046265
≥1
≥1
≥1
≥1
12
0
0
146
624
23320
405310
2806027
≥1
≥1
≥1
≥1
≥1
13
3
9
262
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
4
16
487
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
2
841
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
6
36
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
5
25
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
4
24
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
10
100
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
6
48
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
10
120
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
15
225
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
23
12
144
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
24
20
440
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
25
21
483
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
26
23
529
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
27
35
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
28
34
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
29
44
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
30
56
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all

See Also

I triomino and Z tetrominoI triomino and L pentomino