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 T pentomino

Prime rectangles: ≥ 21.

Smallest rectangle tilings

Smallest rectangle and 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 \ h1-3456789N>0
1-30
4044P
500000
60000000
703232P1616P2828P10861086P
801616C006464P20022002C832832C
90002020P164164P30823082C1090410904P6272862728P
100202202P252252P918918P3356433564C131912131912C558682558682Call
110208208C2828P23582358P≥1≥1C≥1≥1C≥1≥1Call
1206464C488488P62926292P≥1≥1C≥1≥1C≥1≥1Call
13011541154P27682768P2225622256P≥1≥1C≥1≥1C≥1≥1Call
14018081808C862862C5970059700C≥1≥1C≥1≥1C≥1≥1Call
15011521152C70027002P160276160276C≥1≥1C≥1≥1C≥1≥1Call
160≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
170≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
180≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
190≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
200≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallallallall

See Also

I triomino and R pentominoI triomino and U pentomino