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.


P hexomino

Area: 6.

Size: 2x4.

Holes: 0.

Order: 2.

Square order: 6.

Odd order: 11.

Prime rectangles: 5.

Some facts:

Smallest rectangle tilings

Smallest rectangles (2x6, 3x4):

Smallest square (6x6):

Smallest odd rectangle (6x11):

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
N>0
1
0
2
0
0
3
0
0
0
4
0
0
2
0
5
0
0
0
0
0
6
0
2
0
8
0
48
7
0
0
0
0
0
0
0
8
0
0
4
0
0
202
0
0
9
0
0
0
32
0
0
0
2444
0
10
0
0
0
0
0
880
0
0
3760
0
11
0
0
0
0
0
32
0
0
0
0
0
12
0
4
8
114
72
4410
3512
85926
≥1000
≥1000
≥1000
≥1000
13
0
0
0
0
0
192
0
0
0
0
0
≥1000
0
14
0
0
0
0
0
19920
0
0
≥1000
0
0
≥1000
0
0
15
0
0
0
456
0
1024
0
1379926
0
≥1000
0
≥1000
0
≥1
0
16
0
0
16
0
0
91282
0
0
≥1000
0
0
≥1000
0
0
≥1
0
17
0
0
0
0
0
7296
0
0
0
0
0
≥1000
0
0
0
0
0
18
0
8
0
1712
384
431496
131232
≥1
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
0
0
0
39680
0
0
0
0
0
≥1000
0
0
0
0
0
≥1
6k
20
0
0
32
0
0
1989570
0
0
≥1000
0
0
≥1000
0
0
≥1
0
0
≥1
3k
N>0
x
6k
4k
3k
6k
all
6k
3k
2k
3k
6k
all
6k
3k
2k
3k
6k
all

Smallest prime reptiles

Smallest prime reptile (6Px2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
P hexomino
1
1
4
13337
3920564
≥12230590464

See Also

O hexominoT3 hexomino