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.


U pentomino and Y pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (3x10):

Smallest square (10x10):

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
3
?
?
0
4
?
?
0
0
5
?
?
0
0
0
6
?
?
0
0
0
0
7
?
?
0
0
0
0
0
8
?
?
0
0
0
0
0
0
9
?
?
0
0
0
0
0
0
0
10
?
?
2
0
10
22
36
180
810
3370
11
?
?
0
0
12
0
0
0
0
7710
?
12
?
?
0
0
4
0
0
0
0
≥1
?
?
13
?
?
0
0
8
0
0
0
0
≥1
?
?
?
14
?
?
0
0
56
0
0
0
0
≥1
?
?
?
?
15
?
?
0
2
40
60
736
9016
86572
≥1
≥1
≥1
≥1
≥1
≥1
16
?
?
0
0
18
0
0
0
0
≥1
?
?
?
?
≥1
?
17
?
?
0
0
24
0
0
0
0
≥1
?
?
?
?
≥1
?
?
18
?
?
0
0
64
0
0
0
0
≥1
?
?
?
?
≥1
?
?
?
19
?
?
0
0
100
0
0
0
0
≥1
?
?
?
?
≥1
?
?
?
?
20
?
?
4
2
418
1382
21756
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1

Smallest prime reptiles

Smallest prime reptiles (5Ux4, 5Yx4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
U pentomino
0
0
0
2
1926
76235
≥16000
Y pentomino
0
0
0
1
1303
83587
≥350000

See Also

U pentomino and X pentominoU pentomino and A hexomino