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 I pentomino

Prime rectangles: ≥ 20.

Smallest rectangle tilings

Smallest rectangle (1x8):

Smallest square (5x5):

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 \ h1234567N>0
100
20000
3000000
400000000
500000088P2424P
6000022P44P4646P208208C
7000033P44P132132P471471C660660C
822P44C1212C100100C530530C27122712C1256412564Call
900002323P5858P11611161C95679567C3544235442Call
1000003636P202202C28482848C2939629396C132684132684Call
1133P99C8181C921921C1010010100C125677125677C10462651046265Call
120000146146C624624C2332023320C405310405310C28060272806027Call
1333P99C262262C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
1444P1616C487487C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
150022P841841C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
1666C3636C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
1755P2525C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
1844P2424C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
191010C100100C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
2066P4848C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
211010C120120C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
221515C225225C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
231212P144144C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
242020C440440C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
252121C483483C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
262323C529529C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
273535C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
283434C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
294444C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
305656C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1Call
N>0allallallallallallall

See Also

I triomino and Z tetrominoI triomino and L pentomino