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 U pentomino

Prime rectangles: ≥ 26.

Smallest rectangle tilings

Smallest rectangle (4x7):

Smallest square (7x7):

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 \ h1-345678910N>0
1-30
4000
500000
60000000
7022P22P009898P
800022P1818P122122C410410P
900088P6262P262262C26002600P1613616136P
1002222P4040P144144P35823582C1227612276C7018670186C585068585068C
11044P3030P650650P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
12000130130P19961996P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
130162162P462462P50545054P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1405454C362362C1596815968P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
15088P14561456C4529445294P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
16010081008P43864386C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
170480480C38863886C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
180132132C1396613966C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
19057485748P3802238022C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
20035403540C3842838428C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallallallallall

See Also

I triomino and T pentominoI triomino and V pentomino