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.


T tetromino and U pentomino

Prime rectangles: ≥ 19.

Smallest rectangle tilings

Smallest rectangle and smallest square (3x3):

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
4
4
0
0
0
0
5
0
0
0
0
0
6
0
0
16
0
2
260
7
0
0
0
0
0
4
0
8
0
0
0
0
0
68
0
0
9
0
0
64
0
0
4244
52
2
284272
10
0
0
0
0
0
138
8
1180
10474
9970
11
0
0
0
0
0
1692
1116
2568
732
64254
469480
12
0
0
256
0
2
69332
15978
21378
≥1
≥1
≥1
≥1
13
0
0
0
0
32
3528
568
13048
≥1
≥1
≥1
≥1
≥1
14
0
0
0
0
8
37170
1262
22406
≥1
≥1
≥1
≥1
≥1
≥1
15
0
0
1024
0
0
1132972
8524
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
0
0
0
0
79770
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
0
0
0
0
763216
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
0
4096
0
140
18519634
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
0
0
256
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
0
0
0
64
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
16384
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
22
0
0
0
0
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
23
0
0
0
0
2888
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
24
0
0
65536
0
15740
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
25
0
0
0
0
25184
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1

Smallest prime reptiles

Smallest prime reptiles (4Tx3, 5Ux3):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
T tetromino
0
0
256
0
162
≥4815104840
≥1
U pentomino
0
0
1024
0
21418
≥1251927258400
≥1

Smallest common multiples

Smallest common multiple (area 40):

Common multiples' solutions count (excluding symmetric)

area
20
40
solutions
?
≥1

See Also

T tetromino and T pentominoT tetromino and V pentomino