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 Y pentomino

Prime rectangles: ≥ 16.

Smallest rectangle tilings

Smallest rectangle (2x7):

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 \ h123456N>0
10
2000
300000
40000088P
500088P6868P568568P
60001616P356356P37323732C3915239152C
7022P6464P17041704C2146821468C359450359450C?
8066P164164P73027302C139286139286C33713673371367C?
901616P440440P3033030330C770000770000C3017474630174746C?
1003636P11741174C122774122774C48005724800572C≥1≥1C?
110≥1≥1P≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
120≥1≥1P≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
130≥1≥1P≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
140≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
N>0xallallallallall

See Also

Dominoes and X pentominoDominoes and Z pentomino