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.


I2 octomino

Area: 8.

Perimeter: 12.

Size: 2x4.

Is rectangular: yes.

Is convex: yes.

Holes: 0.

Order: 1.

Square order: 2.

Odd order: 1.

Prime rectangles: 1.

Smallest rectangle tilings

Smallest rectangle and smallest odd rectangle (2x4):

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 \ h12345678910111213141516
10
200
3000
4011P022C
50000000
600033C0000
700000000000
8011C055C001111C003636C
9000000000000000
1000088C0000009595C0000
110000000000000000000
12011C01313C004141C00281281C00≥1000≥1000C00≥1000≥1000C
1300000000000000000000000
140002121C000000781781C000000≥1000≥1000C0000
15000000000000000000000000000
16011C03434C00153153C00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C
N>0x4kx?????????????

Smallest prime reptiles

Smallest prime reptile (8I2x2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I2 octomino15P41P2245C185921P

See Also

I1 octominoJ1 octomino