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.


I triomino and P pentomino

Prime rectangles: ≥ 21.

Smallest rectangle tilings

Smallest rectangles and smallest square (2x8, 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 \ h123456789N>0
10
2000
300000
40000044P
50000088P7272P
600044P5656P344344P20562056C
70002424P9090P10531053P1117611176C5529255292C
8066P5656P356356C58385838C6583465834C569464569464C75906807590680C
9000104104P11021102C2002620026C352690352690C45865464586546C7877466878774668C≥1≥1C
10000224224P≥1000≥1000C??????????all
1101212P432432P≥1000≥1000C??????????all
12000768768C≥1000≥1000C??????????all
1302020P≥1000≥1000C≥1000≥1000C??????????all
1402020P≥1000≥1000C≥1000≥1000C??????????all
15000≥1000≥1000C≥1000≥1000C??????????all
1606060C≥1000≥1000C≥1000≥1000C??????????all
1703030P≥1000≥1000C≥1000≥1000C??????????all
1805656P≥1000≥1000C≥1000≥1000C??????????all
190140140C≥1000≥1000C≥1000≥1000C??????????all
2004242P≥1000≥1000C≥1000≥1000C??????????all
210224224C≥1≥1C≥1≥1C??????????all
220280280C≥1≥1C≥1≥1C??????????all
230200200P≥1≥1C≥1≥1C??????????all
240672672C≥1≥1C≥1≥1C??????????all
250504504C≥1≥1C≥1≥1C??????????all
N>0xallallallallallallallall

See Also

I triomino and N pentominoI triomino and R pentomino