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 (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 \ h123456789101112N>0
10
200
3000
40022P0
500000
6022P088C004848C
700000000
80044C00202202C00
90003232C000024442444C0
1000000880880C0037603760P0
11000003232P00000
12044C88C114114C7272C44104410C35123512C8592685926C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
1300000192192C00000≥1000≥1000C6k
14000001992019920C00≥1000≥1000C00≥1000≥1000C3k
15000456456C010241024C013799261379926C0≥1000≥1000C0≥1000≥1000C2k
16001616C009128291282C00≥1000≥1000C00≥1000≥1000C3k
170000072967296C00000≥1000≥1000C6k
18088C017121712C384384P431496431496C131232131232C≥1≥1C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
19000003968039680C00000≥1000≥1000C6k
20003232C0019895701989570C00≥1000≥1000C00≥1000≥1000C3k
N>0x6k4k3k6kall6k3k2k3k6kall

Smallest prime reptiles

Smallest prime reptile (6Px2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
P hexomino11P4P13337C3920564P≥12230590464C

See Also

O hexominoT3 hexomino