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.


P1 octomino

Area: 8.

Size: 2x6.

Holes: 0.

Order: 2.

Square order: 8.

Prime rectangles: ≥ 5.

Smallest rectangle tilings

Smallest rectangle (2x8):

Smallest square (8x8):

Rectangle tilings' solutions count (including symmetric)

Blue number (P) - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number (W) - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Red number (C) - 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 \ h12345678910111213141516N>0
10
200
3000
400000
5000000
600000000
70000000000
8022P044C088C003232C
900000000000000
100000000000128128C0000
11000000000000000000
1200022P00000388388C000000≥1000≥1000C
130000000000000000000000
140000000000≥1000≥1000C000000000000
1500000000000000000000000000
16044C01616C06464C00≥1000≥1000C256256P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
170000000000???????????????????
180000000000???????????????????
190000000000???????????????????
200001616C00000???????????????????
210000000000???????????????????
220000000000???????????????????
230000000000???????????????????
24088C06868C0584584C00???????????????????
250000000000???????????????????
260000000000???????????????????
270000000000???????????????????
280009696C00000???????????????????
290000000000???????????????????
300000000000???????????????????
310000000000???????????????????
3201616C0304304C0≥1000≥1000C128128P??256256C???????????????
33000??0???????????????????????
34000??0???????????????????????
35000??0???????????????????????
36000??0???????????????????????
37000??0???????????????????????
38000??0???????????????????????
39000??0???????????????????????
400??0??0???????????????????????
41000??0???????????????????????
42000??0???????????????????????
43000??0???????????????????????
44000??0???????????????????????
45000??0???????????????????????
46000??0???????????????????????
47000??0???????????????????????
480??0??0??4300843008P???????????????????
49000??0???????????????????????
50000??0???????????????????????
51000??0???????????????????????
52000??0???????????????????????
53000??0???????????????????????
54000??0???????????????????????
55000??0???????????????????????
560??0??0???????????????????????
57000??0???????????????????????
58000??0???????????????????????
59000??0???????????????????????
60000??0???????????????????????
61000??0???????????????????????
62000??0???????????????????????
63000??0???????????????????????
640??0??0??≥1≥1C???????????????????
N>0x8kx?x???????????

Smallest prime reptiles

Smallest prime reptile (8P1x4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
P1 octomino100528P09001056P≥3200000P≥1P≥1P

See Also

L2 octominoP2 octomino