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.


Monominoes and Dominoes

Prime rectangles: 4.

Smallest rectangle tilings

Smallest rectangle (1x3):

Smallest square (2x2):

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 \ h123N>0
100
20044P
322P1818C130130C
433P6565C811811Call
577P219219C50955095Call
61111C719719C3164531645Call
72020C23342334C196784196784Call
83232C75387538C12223961222396Call
95454C2428924289C≥4132045≥4132045Call
N>0allallall

Smallest prime reptiles

Smallest prime reptiles (1Ox2, 2Ix2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
O monomino??P?P?C
I domino??P?P?C

Smallest common multiples

Smallest common multiple (area 2):

Common multiples' solutions count (excluding symmetric)

area2
solutions1P

See Also

P3 9-ominoMonominoes and I triomino