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.


L1 heptomino

Area: 7.

Perimeter: 16.

Size: 2x6.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 2.

Square order: 28.

Odd order: 27.

Prime rectangles: 2.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (14x14):

Smallest odd rectangle (9x21):

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 \ h1234567891011121314N>0
10
200
3000
40000
500000
6000000
7022P044C088C0
80000001616C0
9000000000
100000003232C000
1100000000000
120000006464C00000
130000000000000
14044C01616C06464C128128C264264C15361536C10961096C1075210752C45624562C≥1000≥1000C≥1000≥1000C
150000000000000≥1000≥1000C?
16000000256256C000000≥1000≥1000C?
170000000000000≥1000≥1000C?
18000000512512C000000≥1000≥1000C?
190000000000000≥1000≥1000C?
2000000010241024C000000≥1000≥1000C?
21088C06464C0512512C043524352C512512P3788837888C92169216C333824333824C≥1000≥1000C≥1000≥1000C?
2200000020482048C000000≥1000≥1000C?
230000000000000≥1000≥1000C?
2400000040964096C000000≥1000≥1000C?
250000000000000≥1000≥1000C?
2600000081928192C000000≥1000≥1000C?
270000000000000≥1000≥1000C?
2801616C0256256C040964096C1638416384C7188871888C26296962629696C13153921315392C124333056124333056C≥143000≥143000C≥1000≥1000C≥1000≥1000C?
N>0x7kx7kx7k2k7k7k7k7k7k7kall

Smallest prime reptiles

Smallest prime reptile (7L1x6):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
L1 heptomino1000012288P1572864P≥1100000P

See Also

I heptominoP1 heptomino