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.


Dominoes and I tetromino

Prime rectangles: 7.

Smallest rectangle tilings

Smallest rectangle (1x6):

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 \ h12345N>0
10
20000
30000
40022P1414P108108C
5066P0490490C0
622P1717C146146C25392539C2218322183C?
703434P01099410994C0?
833P8080C12691269C5248352483C≥1≥1C?
90165165C0≥1≥1C0?
1077P358358C1017110171C≥1≥1C≥1≥1C?
110724724C0≥1≥1C0?
121111C15081508C7939379393C≥1≥1C≥1≥1C?
13030393039C0≥1≥1C0?
142020C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
150≥1≥1C0≥1≥1C0?
163232C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
170≥1≥1C0≥1≥1C0?
N>02kall2kall2k

Smallest prime reptiles

Smallest prime reptiles (2Ix2, 4Ix2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I domino??P?P?C
I tetromino??P?P?C

Smallest common multiples

Smallest common multiple (area 4):

Common multiples' solutions count (excluding symmetric)

area4
solutions1P

See Also

Dominoes and L triominoDominoes and L tetromino