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.


Triominoes

Prime rectangles: ≥ 5.

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
N>0
1
0
2
0
0
3
0
0
8
4
0
0
16
0
5
0
0
58
0
0
6
0
6
156
908
8248
79866
7
0
0
432
0
0
613906
0
8
0
0
1144
0
0
5270088
0
0
9
0
32
3108
41668
1269395
≥1
≥1
≥1
≥1
10
0
0
8206
0
0
≥1
0
0
≥1
0
11
0
0
21896
0
0
≥1
0
0
≥1
0
0
12
0
136
58110
1894428
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
0
154302
0
0
≥1
0
0
≥1
0
0
≥1
0
14
0
0
409316
0
0
≥1
0
0
≥1
0
0
≥1
0
0
15
0
538
1086378
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
0
2881488
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
17
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
18
0
2066
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
20
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
21
0
7824
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
23
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
24
0
29424
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
x
3k
all
3k
3k
all
3k
3k
all
3k
3k
all
3k
3k
all
3k
3k
all
3k
3k

Smallest prime reptiles

Smallest prime reptiles (3Ix2, 3Lx2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
1²
2²
3²
4²
I triomino
0
6
3108
1894428
L triomino
0
6
2656
1665413

Smallest common multiples

Smallest common multiple (area 6):

Common multiples' solutions count (excluding symmetric)

area
3
6
solutions
0
≥2

See Also

L1 20-ominoI triomino