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.


P2 octomino

Area: 8.

Size: 2x5.

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 \ h1234567891011121314151617181920N>0
10
2000
30000
4000000
50000000
6000000000
70000000000
8022P044C088C03232C
90000000000000
1000000000009696C0??
110000000000000??00
120000000000256256C0??00??
130000000000000??00??00
140000000000640640C0??00??00??
150000000000000??00??00????
16044C01616C06464C0≥1000≥1000C0≥1≥1C00≥1≥1C00≥1≥1C??≥1≥1C
170000000000000??00??00????????
180000000000≥1000≥1000C0??00??00????≥1≥1C????
190000000000000??00??00????????????
200000000000≥1000≥1000C0??00??00????≥1≥1C??????≥1≥1P
210000000000000??00??00???????????????
220000000000≥1000≥1000C0??00??00????≥1≥1C?????????
230000000000000??00??00???????????????
24088C06464C0512512C0≥1000≥1000C0≥1≥1C00≥1≥1C00≥1≥1C??≥1≥1C?????????
250??0??0??0??0??00??00???????????????
260??0??0??0??0??00??00???????????????
270??0??0??0??0??00??00???????????????
280??0??0??0??0??00??00???????????????
290??0??0??0??0??00??00???????????????
300??0??0??0??0??00??00???????????????
310??0??0??0??0??00??00???????????????
3201616C0??0??0??0??≥1000≥1000P??≥1000≥1000C???????????????
330??0??0??0??0??????00???????????????
340??0??0??0??0??????00???????????????
350??0??0??0??0??????00???????????????
360??0??0??0??0??????00???????????????
370??0??0??0??0??????00???????????????
380??0??0??0??0??????00???????????????
390??0??0??0??0??????00???????????????
4003232C0??0??0??0???????????????????????
410??0??0??0??0???????????????????????
420??0??0??0??0???????????????????????
430??0??0??0??0???????????????????????
440??0??0??0??0???????????????????????
450??0??0??0??0???????????????????????
460??0??0??0??0???????????????????????
470??0??0??0??0????????????≥1≥1P?????????
4806464C0??0??0??0??????≥1000≥1000P???????????????
N>0x?x?x?x?x???????????

Smallest prime reptiles

Smallest prime reptile (8P2x4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
P2 octomino1001024P00

See Also

P1 octominoP3 octomino