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.


L triomino and T tetromino

Prime rectangles: 8.

Smallest rectangle tilings

Smallest rectangle (2x5):

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
1
0
2
0
0
3
0
0
0
4
0
0
0
0
5
0
2
0
18
96
6
0
0
0
16
240
972
7
0
2
0
108
1580
10120
119728
8
0
8
0
390
4816
55462
970448
12221214
9
0
2
0
818
24800
368432
9654948
≥1
≥1
10
0
12
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
11
0
26
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
12
0
16
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
50
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
0
84
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
82
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
184
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
282
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
348
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
650
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
976
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
all
x
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all

See Also

L triomino and O tetrominoL triomino and Z tetromino