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.


P3 octomino

Area: 8.

Size: 3x4.

Holes: 0.

Order: 2.

Square order: 2.

Prime rectangles: ≥ 4.

Smallest rectangle tilings

Smallest rectangle and smallest square (4x4):

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 \ h1-3456789101112N>0
1-30
4044P
50000
6000000
700000000
801616C0044P00270270C
9000000000000
1000000000160160C0000
110000000000000000
1206464C00000046884688C000000≥100≥100C
13000000000000000000?
140000000047284728C00000000?
15000000000000000000?
160256256C88P1616C128128P8371683716C≥100≥100C≥100≥100C≥100≥100C≥100≥100C?
17000000000000000000?
1800000000122688122688C000000???
190000000000000000???
20010241024C00000015343761534376C000000???
210000000000000000???
2200000000≥1000≥1000C000000???
230000000000000000???
240≥1000≥1000C006464C00≥1000≥1000C00≥100≥100C?????
250000000000?????????
2600000000≥1000≥1000C?????????
270000000000?????????
280≥1000≥1000C000000≥1000≥1000C?????????
290000000000?????????
3000000000≥1000≥1000C?????????
3100000000???????????
320≥1000≥1000C6464C256256C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1C???
N>0x4k????????

Smallest prime reptiles

Smallest prime reptile (8P3x4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²10²11²12²13²14²
P3 octomino10075008P23632P≥100000P≥100000P≥100000P≥100000P≥100000P≥100000P≥100000P≥100000P≥100000P

See Also

P2 octominoA 9-omino