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 and N pentomino

Prime rectangles: 40.

Smallest rectangle tilings

Smallest rectangle (5x11):

Smallest square (8x8):

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
1-4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-4
0
5
0
0
6
0
0
0
7
0
0
0
0
8
0
0
0
4
16
9
0
0
0
4
52
24
10
0
0
12
4
120
452
3166
11
0
8
8
24
420
2152
≥1000
≥1
12
0
10
28
240
1512
9804
≥1000
≥1
≥1
13
0
0
16
260
5000
21520
≥1000
≥1
≥1
≥1
14
0
4
205
652
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
15
0
92
288
2472
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
16
0
150
919
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
17
0
20
1066
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
86
4128
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
852
8856
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
1522
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
460
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
0
1346
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
23
0
7900
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
24
0
14612
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
25
0
8560
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
26
0
21472
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
27
0
82100
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
28
0
157994
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
29
0
168084
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
30
0
380054
≥1
≥1
≥1
≥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

See Also

I tetromino and L pentominoI tetromino and P pentomino