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.


I triomino and Z pentomino

Prime rectangles: 24.

Smallest rectangle tilings

Smallest rectangle (6x7):

Smallest square (7x7):

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
1-4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-4
0
5
0
0
6
0
0
0
7
0
0
4
4
8
0
0
14
8
0
9
0
6
36
478
2248
10328
10
0
0
126
232
1310
60790
72192
11
0
2
378
556
2010
271586
392026
≥1
12
0
80
984
19488
136100
≥1
≥1
≥1
≥1
13
0
0
2722
8376
≥1
≥1
≥1
≥1
≥1
≥1
14
0
32
7454
22156
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
738
19284
596730
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
0
50076
254662
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
348
130462
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
5864
332752
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
16
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
3176
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
43014
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
0
360
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
23
0
26160
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
24
0
300468
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
25
0
4994
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
26
0
201718
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
27
0
2032028
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
x
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all

Smallest prime reptiles

Smallest prime reptiles (3Ix5, 5Zx2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I triomino
0
0
0
0
738
332752
Z pentomino
0
2
0
1570
2914271
≥1

Smallest common multiples

Smallest known common multiple (area 30):

Common multiples' solutions count (excluding symmetric)

area
15
30
solutions
?
≥1

See Also

I triomino and Y pentominoI triomino and T1 hexomino