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 12-omino

Area: 12.

Perimeter: 18.

Size: 3x6.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 8.

Square order: 12.

Prime rectangles: ≥ 2.

Smallest rectangle tilings

Smallest rectangle (8x12):

Smallest square (12x12):

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 \ h1-789-111213-151617-192021-2324N>0
1-70
800
9-11000
12022P022P
13-15000000
1600066C000
17-19000000000
200001010C000000
21-23000000000000
24044C02222C04040C0302302C012601260C
2500000000000000?
2600000000000000?
2700000000000000?
280004242C000000049584958C?
2900000000000000?
3000000000000000?
3100000000000000?
320008686C00000002484424844C?
3300000000000000?
3400000000000000?
3500000000000000?
36088C0170170C0272272C075787578C0107350107350C?
3700000000000000?
3800000000000000?
3900000000000000?
40000342342C0000000477548477548C?
4100000000000000?
4200000000000000?
4300000000000000?
44000682682C000000021901582190158C?
4500000000000000?
4600000000000000?
4700000000000000?
4801616C013661366C018561856C0194174194174C097364289736428C?
N>0x12kx?x?x?x?

Smallest prime reptiles

Smallest prime reptile (12L1x12):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²10²11²12²13²14²15²
L1 12-omino≥10000000000≥4000000P000

See Also

P1 11-ominoO1 12-omino