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.


O tetromino and Z pentomino

Prime rectangles: ≥ 6.

Smallest rectangle tilings

Smallest known rectangle and 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
19
20
1
0
2
0
0
3
0
0
0
4
0
0
0
0
5
0
0
0
0
0
6
0
0
0
0
0
2
7
0
0
0
0
0
0
0
8
0
0
0
0
0
4
0
8
9
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
6
0
21
0
62
11
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
14
0
55
0
224
0
≥1000
13
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
26
0
122
0
726
0
≥1000
0
≥1
15
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
16
0
0
0
0
0
42
0
305
0
≥1000
0
≥1000
0
≥1
?
≥1
17
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
?
?
18
0
0
0
0
0
80
0
727
0
≥1000
0
≥1000
0
≥1
?
≥1
?
≥1
19
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
20
0
0
0
0
0
146
0
≥1000
0
≥1000
0
≥1000
0
≥1
?
≥1
?
≥1
?
≥1

See Also

O tetromino and Y pentominoO tetromino and A hexomino